Algebra Review MCQs
89. CSET! Using prime numbers x, y, and z all less than 35, how many possible numbers can 2^x*7^y*11^z represent?
http://youtu.be/fjynzeypAMM Note: written solution has an error, mistakenly saying 21 and 23 are prime (I know; I was going too fast! sorry!) so the answer should be 11^3. It is fixed in the video solution in an annotation, but if you're viewing the videos on a phone or ipad you won't be able to see any annotations.
86. CSET! If f(x) = ax^4 + bx^3 + cx^2 + dx + e and f(x)/(x+g) = fx^3 + gx^2 + hx + k, which must be true? a. g is a rational number b. x - g is a factor f(x) c. g is a root of f(x) d. -g is a root of f(x)
http://youtu.be/wRgdmImqPR0
78. CSET! Consider species of fish A, B, and C, such that species A feeds on species B which in turn feeds on species C. The size of species A is given by A(x) = 1000 + √(2x) and that of species B by B(y) = 2500 + √(y) where x and y represent the number of fish in species B and C respectively. Find the size of species A when the size of species C is 6,250,000. a. 1070 b. 1100 c. 1166 d. 1234
http://youtu.be/zeOMXLJE6RQ
100. CSET! A 4th degree polynomial with real coefficients has leading coefficient 2. Two of its roots are 4i and 7. Given that it passes through the point (3, -400), find the remaining root(s) and the equation of the polynomial. Write your answer in standard form.
https://drive.google.com/file/d/1EEsfuZyJE0GG3PUow7OrZdgxgMjK2gsC/view?usp=sharing
101. CSET! A 5th degree polynomial with real coefficients has leading coefficient 1. Three of its roots are -2i, -3, and 1. Given that it passes through the point (-1, 140), find the remaining root(s) and the equation of the polynomial. (You may leave your answer in factored form.)
https://drive.google.com/file/d/1EEsfuZyJE0GG3PUow7OrZdgxgMjK2gsC/view?usp=sharing
21. CSET! A parabola has x-intercepts -3 and 5. If the maximum value of the function is 3, find its equation.
https://www.youtube.com/watch?v=0j6jdoPWHmg&feature=youtu.be
39. If i is a root of g(x) = 7x^112 - 6x^75 + ax^65 + bx^62 - 4, then find the value of a and b.
https://www.youtube.com/watch?v=6CRQpytXpFo&feature=youtu.be
23. CSET! What is the range of f(x) = 3x^2 - 4x + 5?
https://www.youtube.com/watch?v=6oR2wxmtzLY&feature=youtu.be
56. CSET! Given two vectors a and b such that a = <√2/2, -√2/2> and b = -16a, find the magnitude and direction of b.
https://www.youtube.com/watch?v=VlFeXFZQBD4&feature=youtu.be
18. CSET! Consider a point P on the curve y = x^4. What is the slope of the segment OP as a function of x? (O is the origin.)
https://www.youtube.com/watch?v=WEUxJWzzTaU&feature=youtu.be
27. CSET! If f(x) = 2x^2 - 3x + 5 and g(x) = bx - 2, find b such that f(x) and g(x) intersect at one point only.
https://www.youtube.com/watch?v=d_4ebDh1A1w&feature=youtu.be
15. CSET! What is the point of intersection of f(x) = (5/2)x + 2/3 and its inverse?
https://www.youtube.com/watch?v=djGWSBc6Kfk&feature=youtu.be Note!!! Short-cut -- can eliminate any multiple choice that don't have matching x and y
8. CSET! If 116/15 is written as a ratio of integers, a/b, with a and b relatively prime, what is the value of a + b?
https://www.youtube.com/watch?v=nyzQN8gdtZU&feature=youtu.be
44. CSET! Simplify (x^-3 - y^-3)/((x^-2) - 7(xy)^-1 + 6y^-2)
https://www.youtube.com/watch?v=o7UIuM-GQ08&feature=youtu.be
60. Find the product AB, A = [2 4][7 -1], B = [-3 0][2 5].
[2 20][-23 -5] no video solution linked
64. Find the determinant [2 -4 1][3 0 9][-1 5 7].
45 no video solution
58. CSET! Given A = [-2 5 0 4][3 -4 6 -1], B = [-2 4][3 1][5 -3], C = [-6][8] which of the following products exist? a. AB b. AC c. BC d. CA
C. https://www.youtube.com/watch?v=w9dyJ7Xi8bc&feature=youtu.be
81. CSET! The first step in the proof of n! ≤ n^n for all positive integers is to show it holds for n = 1. Using induction, a subsequent step is a. For some n > 1, (n + 1)! ≤ (n + 1)^(n + 1) b. If n! > n^n, a contradiction follows c. For some n > 1, n! > n^n d. If n! ≤ n^n, then (n + 1)! ≤ (n + 1)^(n + 1)
http://youtu.be/_TKIZ13AD1E
1. CSET! What is the greatest common factor (GCF) of 4860, 5148, 6372, 6894, 7236?
a. 6 b. 18 c. 24 d. 54 https://www.youtube.com/watch?v=uXLELqd8A7M&feature=youtu.be
50. CSET! What is the absolute value of the difference between the solutions of 4^(x^2)/(4^x)^2 = 64?
https://www.youtube.com/watch?v=bdtdlBRs16c&feature=youtu.be
96. CSET! Determine if it's possible to form a triangle if it has the given side lengths. a) 5, 9, 1000 b) 5, 9, 10 c) 6, 7, 13 d) 4,4, 6
Solution: Triangle Inequality Theorem: The sum of the two smaller sides must be larger than the third Answers: a) no b) yes c) no d) yes
2. CSET! What is the greatest common factor (GCF) of 4728, 5904, 6168, 6744, 7272?
a. 12 b. 16 c. 18 d. 24 https://www.youtube.com/watch?v=oPdZWVzUbzw&feature=youtu.be
70. CSET! Expand (x + y)^6.
http://youtu.be/7-x6IhYhU70
77. CSET! What shape does the graph |y| + |x| ≤ 3 resemble? a. isosceles triangle b. equilateral triangle c. square d. pentagon
http://youtu.be/FQn0PKkiAY8
82. CSET! Let f be the piecewise function, f(n) = n+5 if n is odd, n/2 if n is even If f(f(k)) = 25 and k is odd, find k.
http://youtu.be/KF0w9fzxFGg
72. CSET! Find the fifth term of (x - 3y)^6.
http://youtu.be/OlzOgtIxJCI
85. CSET! If f(x) = y = x^2, what is one of the roots of f(x) if it is translated 2 positive units in the x direction and 1 positive unit in the y direction?
http://youtu.be/Pyn2hQuICFY
88. CSET! Graph on an x-y coordinate plane: The difference between x and y is no greater than 3.
http://youtu.be/bGjSPdo7omw
80. CSET! A regular octagon is inscribed inside a square ABCD with sides 2 cm. Find the length of the side of the polygon.
http://youtu.be/tOuDamy6tLI
99. CSET! A 3rd degree polynomial has real coefficients with leading coefficient 4. Given one of its roots is 3i and it passes through the point (1, -240), find the remaining root(s) and the equation of the polynomial. Write your answer in standard form.
https://drive.google.com/file/d/1EEsfuZyJE0GG3PUow7OrZdgxgMjK2gsC/view?usp=sharing
97. CSET! A treasure chest is filled with coins. 2/15 are pennies 1/5 are nickels 1/15 are dimes 1/10 are quarters 1/3 are half dollars coins 1/6 are dollar coins What percent of these coins are 25 cents or more?
https://drive.google.com/file/d/1gAcIBQYtXRaLfzOQeKABU9nYxq1qVeFq/view?usp=sharing
98. CSET! A treasure chest is filled with coins. 1/4 are pennies 5/36 are nickels 5/24 are dimes 1/24 are quarters 1/18 are half dollars coins and the rest are dollar coins What percent of these are 50 cents or more?
https://drive.google.com/file/d/1gAcIBQYtXRaLfzOQeKABU9nYxq1qVeFq/view?usp=sharing
38. If i is a root of g(x) = 2x^4 + 10x^3 + ax^2 + bx - 4, then find the value of a and b.
https://www.youtube.com/watch?v=-Kv4GRjUQzU&feature=youtu.be Note: I make a small error in the video solution (I forget to subtract the 4 so the a should equal - 2) but the written solution is correct.
40. CSET! Sketch the given functions. The actual exam will most likely have a multiple choice question where you match an equation to its graph or vice-versa. a. f(x) = (x + 3)^2(x + 1)^3(x - 2)^5 b. f(x) = -(x + 4)^2(x + 1)(x - 2)^4
https://www.youtube.com/watch?v=02U8DGin64g&feature=youtu.be
25. CSET! If f(x) = √x and g(x) = x^2 + 4x - 12, what is the domain of f(g(x))?
https://www.youtube.com/watch?v=7pmWLMhs0-4&feature=youtu.be
14. CSET! What is the point of intersection of f(x) = 4x + 7 and its inverse?
https://www.youtube.com/watch?v=BBpsytaQUV4&feature=youtu.be
33. CSET! If an eighth degree polynomial with real coefficients has roots 6 + 4i and -27i, how many real zeros could it have?
https://www.youtube.com/watch?v=CzgVfGSsbE8&feature=youtu.be
34. CSET! Find all the roots of f(x) = 3x^3 + 4x^2 + 7x + 2.
https://www.youtube.com/watch?v=E2tcaIHV1lU&feature=youtu.be
19. CSET! Consider a point P on the curve y = ∜x. What is the slope of the segment OP as a function of x? (O is the origin.)
https://www.youtube.com/watch?v=Gksea5W0C8w&feature=youtu.be
10 a) CSET! How many integers between one and one thousand inclusive are multiples of 7 or 11?
https://www.youtube.com/watch?v=HqesZ46UXcY&feature=youtu.be Note: Oops! I make an error in the video solution 1000/77 = 12, not 10! The error is corrected in the written solutions, so be sure to check that. Sorry for any confusion!
57. CSET! Given vectors a = < 5, -3, 4 > and b = < 7, y, z >, find the set of all y and z such that a is perpendicular to b.
https://www.youtube.com/watch?v=IiTpfbwxhgw&feature=youtu.be
17. If point (-7, 3) lies on the graph of the inverse of f(x) = 5x^2 + x + a, find a.
https://www.youtube.com/watch?v=JQTSAVSXcaE&feature=youtu.be
52. CSET! Find the magnitude and direction of the vector v = -√3i + j.
https://www.youtube.com/watch?v=KNcv-d1ASjs&feature=youtu.be note: the video solution is correct; in the written solution, the numbers are correct, but I accidentally switch the labeling of the direction and magnitude
63. Find the determinant [-2 3 1][0 4 -3][2 5 -1].
https://www.youtube.com/watch?v=LCN6KJUhX-M&feature=youtu.be
5. CSET! If the prime factorization of x is ab^2c^3 and that of y is b^3c^2, what is the greatest common divisor of x and y? the least common multiple?
https://www.youtube.com/watch?v=LinFgAx5aQA&feature=youtu.be
26. CSET! If f(x) = √x and g(x) = -x^2 + x + 20, what is the domain of f(g(x))?
https://www.youtube.com/watch?v=N1j24we-87k&feature=youtu.be
68. Solve the following system of equations using an augmented matrix and Gaussian elimination. x - y + 2z = -3 2x + y - z = 0 -x + 2y - 3z = 7
https://www.youtube.com/watch?v=POrPGGeEwB4&feature=youtu.be
53. CSET! If vector a has magnitude 10 and direction 60°, and vector b has magnitude 20 with direction 30°, find vector a + b in component form.
https://www.youtube.com/watch?v=QjH5y1rl9VI&feature=youtu.be practice 30-60-90 triangle reasoning
20. CSET! A parabola has x-intercepts 1 and 5. If the minimum value of the function is -4, find its equation.
https://www.youtube.com/watch?v=Uq2cieCuGys&feature=youtu.be
22. CSET! For each of the following cases draw a graph of f(x) = ax^2 + bx + c that follows the given condition. (Not multiple choice! Draw possible graphs for each scenario) a. b^2 - 4ac > 0 b. b^2 - 4ac = 0 c. b^2 - 4ac < 0
https://www.youtube.com/watch?v=YDgiI503dFI&feature=youtu.be
6. CSET! If the prime factorization of x is a^5c and that of y is a^4b^3c^2, what is the greatest common divisor of x and y? the least common multiple?
https://www.youtube.com/watch?v=YzDrknp6eGI&feature=youtu.be
42. CSET! Solve (x + 9)^2(x^2 - 5x + 6) ≤ 0
https://www.youtube.com/watch?v=ZFUs_FKPsGw&feature=youtu.be
47. CSET! The future value A of an initial quantity P after t years is given by A = P(1.05)^t. How long does it take P to double?
https://www.youtube.com/watch?v=ZOdCuZc_UoM&feature=youtu.be
48. CSET! The future value A of an initial quantity P after t years is given by A = P(1.06)^t. How long does it take P to quadruple?
https://www.youtube.com/watch?v=Zgvhnm14J8E&feature=youtu.be
30. CSET! What is the highest number of points of intersection between a seventh degree polynomial and a third degree polynomial?
https://www.youtube.com/watch?v=_M8JRmFkLX0&feature=youtu.be
16. If point (5, -2) lies on the graph of the inverse of f(x) = 3x^4 - 4x + a, find a.
https://www.youtube.com/watch?v=_wneMyZUvtM&feature=youtu.be
46. Solve: a. log(1 - x) = 4 w/ base 2 b. ln(2x - 3) = 14 c. 10^(3x - 5) = 7 d. e^(3x/4) = 10
https://www.youtube.com/watch?v=cmogomWojs0&feature=youtu.be
41. CSET! Solve (x - 4)(x^2 - 6x - 7) < 0.
https://www.youtube.com/watch?v=dFNx6ZYyC3c&feature=youtu.be
9. CSET! How many integers between one and five hundred inclusive are multiples of 3 or 5?
https://www.youtube.com/watch?v=dSQPVcaTSa4&feature=youtu.be
54. CSET! If vector u has magnitude 8 and direction 45°, and vector v has magnitude 20 with direction 150°, find vector u+ v in component form.
https://www.youtube.com/watch?v=rcaeT_PP4VI&feature=youtu.be practice 45-45-90 triangle reasoning
67. Solve the following system of equations using an augmented matrix and Gaussian elimination. x - 2y + z = 7 3x - 5y + z = 14 2x - 2y - z = 3
https://www.youtube.com/watch?v=ru_M7VSNIzc&feature=youtu.be
36. CSET! If (x - 2) is a factor of x^5 + kx - 4, what is a possible value of k?
https://www.youtube.com/watch?v=tayclx2eURc&feature=youtu.be
49. CSET! A current population of 500,000 increases exponentially. What is the population after t years if it increases 6% twice a year? a. P(t) = 500,00(1.03)^t b. P(t) = 500,000(1.06)^(t/2) c. P(t) = 500,000(1.06)^2t d. P(t) = 500,000(1.03)^2t
https://www.youtube.com/watch?v=vexnGfZovSY&feature=youtu.be
59. Find the product AB, A = [2 4][3 -1], B = [3 -2 7][6 0 -5].
https://www.youtube.com/watch?v=wosMuUIPVQk&feature=youtu.be
61. Find the determinant [1 6][2 7].
https://www.youtube.com/watch?v=xJS6sMksUQg&feature=youtu.be
62. Find the determinant [-14 -3][2 -2].
https://www.youtube.com/watch?v=xJS6sMksUQg&feature=youtu.be
37. CSET! If (x + 3) is a factor of x^3 + kx - 11, what is a possible value of k?
https://www.youtube.com/watch?v=zK7KTeqv9-A&feature=youtu.be
66. CSET! Suppose A = [a11 a12 a13][a21 a22 a23][a31 a32 a33] and B = [b11 b12 b13][b21 b22 b23][b31 b32 b33] (numbers represent element positions in matrix) and A times [x][y][z] = [e][f][g]. If matrix B is the inverse of matrix A, find the solution for y.
https://www.youtube.com/watch?v=zNWQGOpJQZ0&feature=youtu.be
4. CSET! What is the least common multiple (LCM) of 36, 54, 60, and 90?
https://www.youtube.com/watch?v=zUAtt4bXbRU&feature=youtu.be
73. CSET! Find the tenth term of (2x + y)^12.
https://youtu.be/JjIqeYrzK5I
13. CSET! Consider a set S of numbers of the form a + b√2 under addition and multiplication, where a, b ϵ M, a subset of the complex numbers. Which is true about S?
a. If M is the set of positive integers, S is a ring with multiplicative identity 1 + √2 b. If M is the set of integers, S is a field with additive inverse -a - b√2, and multiplicative inverse a and b = 0 c. If M is the set of rational numbers, S is a field with additive inverse -a - b√2 and multiplicative inverse ((a-b√2)/(a^2-2(b^2))), a and b ≠ 0 d. If M is the set of real numbers, S is a ring with multiplicative inverse (a-2b)/((a^2)√2 + b^2) https://www.youtube.com/watch?v=H3rvnQ2cNz8&feature=youtu.be
10 b) CSET! Multiple choice: Are there more real numbers or rational numbers between 0 and 1?
a. More real b. More rational c. Same d. The sets cannot be compared Solution: Trust the CSET to ask a question that made Cantor go insane! While the answer might seem obvious when you see it -- the answer is a, more real -- the proof is anything but obvious, and dealing with infinities is often very counterintuitive. If you're curious, here's a detailed explanation from Dr. Math. Dr. Math is an excellent resource for juicy questions such as this. http://mathforum.org/library/drmath/view/52393.html
69. CSET! Given the set of equations x1 + x2 + 2x3 = a1 x1 + x3 = a2 2x1 + x2 + 3x3 = a3 which of the following conditions must be met to ensure the system has at least one solution? a. a3 = a1 + a2 b. 2a1 = a3 c. a1 = a2 d. a1 = a2 = a3
a. a3 = a1 + a2 https://www.youtube.com/watch?v=mKdpRTHvgxA&feature=youtu.be
91. CSET! A number greater than 5000 but less than 6000 has prime factors 2^x3^y5^z such that x, y, z > 0. A possible value of x + y + z is: a. 5 b. 8 c. 11. d. 18
b. 8 http://youtu.be/MbXJe6oAn2Y
55. Find the cosine of the angle between the vectors a = <2, - 1 > and b = < 6, 4>.
cos theta = (4√65)/65 no video solution
71. CSET! Expand (2d + 3)^5.
http://youtu.be/DWha0dIcDeI
94. CSET! Order the following numbers from least to greatest: 3, 3.14, pi, e, i, -9, 0
i < -9 < 0 < e < 3 < 3.14 < 𝝅 Note: I was particularly peeved when I heard about the imaginary numbers in this problem. It's specifically listed in the official CSET topic guidelines that you're supposed to know the set of complex numbers are a field, but not an ordered field. I found several sources saying that, yes, you can impose a logical order to them, but that order is not particularly mathematically useful. Fortunately, (if I'm correct!), the problem isn't hard and your intuition will serve you fine. The "rule" is basically just alphabetizing. When comparing to complex numbers of the form a + bi, order the real part first, then the imaginary. In the problem above, it would mean all the pure imaginary numbers are less than the real numbers. 𝝅 = 3.141519... e = 2.71 -9 = 3i
12. CSET! Which of the following is a necessary but not sufficient condition in proving that R(x), the set of polynomials with real coefficients, is an algebraic ring?
a. R(x) is commutative under addition b. R(x) is an ordered set c. R(x) is a vector space under multiplication and addition d. the division algorithm holds in R(x) https://www.youtube.com/watch?v=Ll-ceuneJag&feature=youtu.be
11. CSET! Which of the following is a counterexample of the following statement: R(x), the set of polynomials with real coefficients, is an algebraic field under addition and multiplication of polynomials?
a. p(x) = x2 + 2 has real zeros b. p(x) = x2 has no multiplicative inverse in R(x) c. p(x) = x2 + 3x + 7 is irreducible in R(x) d. p(x) = x2 is not a one-to-one function https://www.youtube.com/watch?v=iqgPmYTLhz0&feature=youtu.be
90. CSET! Using prime numbers a, b, c, and d all less than 15, how many possible numbers can 3^a*5^b*13^c*23^d represent?
http://youtu.be/65i5zNcy04s
79. CSET! A swimming pool, rectangular in shape, is surrounded by a walkway of uniform width x. If the outer dimensions of the walkway are 16m by 10m and the area of the pool alone is 112m^2, find x.
http://youtu.be/C_QMu_-lBOY
84. CSET! A cubic polynomial is expressed as the product of three binomials. Which of the real numbers' properties is used to find the real zeros of the polynomial? a. If a*b = 0, then a = 0 and b = 0. b. If a*b = 0, then a = 0 or b = 0. c. For all a and b a^(1/3)*b^(1/3) = (ab)^(1/3). If a ≠ 0, then a^m*a^n = a^(m+n)
http://youtu.be/V57uzskEqNE
76. CSET! Consider the system of inequalities represented by |y| ≤ 4 and y ≤ -2|x| + 8. The interior of which of the following is a solution of the system? a. right triangle b. isosceles triangle c. parallelogram d. isosceles trapezoid
http://youtu.be/e1jDkFUF6MU
87. CSET! Vector a and vector b are two edges of the top face of a cube. What could be the equation for vector c, the edge of the cube as shown? go to packet to see picture a. dot product of a and b b. cross product of a and b c. vector a and b added together d.vector a minus vector b
http://youtu.be/xUPmCHRRcgI
74. CSET! Find the term containing b^6 in the expansion of (a + b^2)^10.
http://youtu.be/y3CW0k3yAbM
83. CSET! HJKL is a parallelogram. Vectors a, b, and c have initial points at H. Vector d has initial point J. Find the following (note c's solution is not a vector shown; just picture it) go to packet to see picture a. a + d b. a + b c. c - d d. d - b
http://youtu.be/yc2g3VxZbac
93. CSET! According to the fundamental theorem of algebra, which of the equations in Exercises 1 and 2 have at least one root? (go to problem set to see full problem)
https://drive.google.com/file/d/0B7UrQE4OBGiLa0FWOXBLVTVIQXM/view?usp=sharing
92. CSET! Carol bought 4 apples and 5 peaches for $8.25. The next day the store had a sale. Apples were each 4 cents cheaper and peaches were each 6 cents cheaper. She bought 5 apples and 4 peaches at the sale rate for $8.05. How much did each apple and each peach cost on day one?
https://drive.google.com/file/d/0B7UrQE4OBGiLcnQwNl9tUEtYWUk/view?usp=sharing
65. CSET! The tickets for a show were $20 for adults, $15 for students, and $10 for children. The first show was attended by 300 people paying $4000. The second show was attended by 450 people. The same number of adults attended both shows, but three times the students and twice the children attended the second show. Write a matrix equation that could be used to find the number of adults who attended the first show. (Don't actually solve!! You get fractional people. Just set it up!)
https://www.youtube.com/watch?v=1-hmceHc3bg&feature=youtu.be
24. CSET! What is the range of f(x) = -x^2 - 8x + 11?
https://www.youtube.com/watch?v=1MhpF78_Ppg&feature=youtu.be
45. Evaluate the following: a. log28 b. log381 c. log100 d. lne5
https://www.youtube.com/watch?v=4kXdHanJpcY&feature=youtu.be
32. CSET! If a ninth degree polynomial with real coefficients has roots 4i and 5 -3i, how many real zeros could it have?
https://www.youtube.com/watch?v=5hLyjEjhu6Y&feature=youtu.be
35. CSET! Find all the roots of f(x) = 3x^4 + 5x^3 + 25x^2 + 45x - 18.
https://www.youtube.com/watch?v=7oq4BE4wrz8&feature=youtu.be
51. CSET! A vector v has magnitude 4 and makes an angle of 20° with the x axis. Find the magnitude and direction of the vector -3v.
https://www.youtube.com/watch?v=QnpcjQ2sCeA&feature=youtu.be
7. CSET! If 4 and 8/30ths is written as a ratio of integers, a/b, with a and b relatively prime, what is the value of a + b?
https://www.youtube.com/watch?v=fW2Ru5_4xes&feature=youtu.be
28. CSET! For what value(s) of k will the parabola y^2 - 6y + x + k = 0 have exactly one y-intercept? Find the intercept.
https://www.youtube.com/watch?v=jZEJN7_xSNg&feature=youtu.be
43. CSET! Simplify (x^-3 + y^-3)/((x^-2) + 4(xy)^-1 + 3y^-2)
https://www.youtube.com/watch?v=jw2E0JiOlpQ&feature=youtu.be
31. CSET! What is the highest number of points of intersection between a fifth degree polynomial and a fourth degree polynomial?
https://www.youtube.com/watch?v=mmusXItlRwQ&feature=youtu.be
3. CSET! What is the least common multiple (LCM) of 24, 30, 48, and 54?
https://www.youtube.com/watch?v=nofJusem4dE&feature=youtu.be
29. CSET! Find the equation of the line with the same x and y intercepts as x^2 + y^2 + 6x - 6y + 9 = 0.
https://www.youtube.com/watch?v=rEJLEF0i6e0&feature=youtu.be
95. CSET! Simplify each of the following. (1-i)^300 (1-i)^208 (1-i)^406
https://youtu.be/QIyXqRb6Gw8
75. CSET! Find the term containing y3 in the expansion of (y + √2)^15.
https://youtu.be/mGn5Ub3Qyxc
