ALGEBRA 2 FINAL
if f(x)= 2x + 12 and g(x)= x^2 -1, solve: f(x) * g(x)
(2x +12)(x^2-1) (2x+12) (x-1)(x-1) (make box w the x-1's) ANSWER;;; (2x+12)(x^2-2x+1)
solve x^2 = 100
+ or - 10
write the polynomial function that has the zeros 2, -2, and 1, that has a leading coefficient of 1
1. (x+2) (x-2) (x-1) 2. make a box with (x-2) (x-1) 3. then make a box with (x+2) and whatever you get from the first box 4. answer: x^3-X^2-5x+2
(3x^3 + 7x^2 - 2x) - (2x^3+6x^2 -1)
1. distributoe the - 2. add the like terms in each parenthesis together 2. you get x^3 + x^2 - 2x + 1
if f(x)= 2x + 12 and g(x)= x^2 -1, solve: f(g(x))
2(x^2-1) + 12 ANSWE::: 2x^2 -2+12
if f(x)= 2x + 12 and g(x)= x^2 -1, solve: f(x) + g(x)
2x +12+x^2-1 ANSWER IS::: x^2+2x+11
Use synthetic division to divide 2x^3 + 5x^2 - 3x +4 by (x+2)
2x^2 + x - 5 + 14/x +2
write the expression as a complex number in standard form (2-12i) + (8+9i)
combine like terms 10-3i
how would you write the following complex number in standard form? -5i (8+71)
distribute the -5i to both 8 and 7i. you would get -40i - 35i^2. replace i^2 with a -1, simplify. you will end with 35-40i
how would you solve a problem like: simplify: (-7a^2b^5c^3)^4
distribute the 4 to everything, to get (-7)^4A^8B^20C^12 ANSWER IS 2401a^8b^20c^12
how would you solve 2(x-5)^2 = 128
divide both sides by 2 and then make a box with (x-5) ^2 then write what you get out and get the right side to equal 0 and then find what two numbers multiply to c and add up to b. write them out in intercept form and the answers would be what you can plug into x to equal zero. for this problem, it would be 13 and -3
how do you do synthetic division?
line the equation up with no x's and a little number on the left with what you are dividing by (you know this from what x is). then, start with the first number. bring it down, multiply it by what your dividing by, add it to the number above, repeat till you get to end. answer all the way to the left is the remainder, next is constant, then add x for the next one, x^2 for the next one, and so on
how do you solve problems like these: (2x - 1) ^ 3
make a 2 by 2 box then make a 3 by 2 box with the answer that you get from the 2 by 2 box
how would you solve a problem like this: the 6th root of 256
make two separate 6 square roots, one w perfect squares and one w left overs. then solve the one w the perfect square and bring the leftovers w it
how would you solve 2 ----- 3+ square root of 5
multiply top and bottom by (3- square root of 5)
evaluate/simplify a\16 ^ 3/2
p/r so square root of 16 to the third, then that is 4 to the third which is 64
if f(x)= 2x + 12 and g(x)= x^2 -1, solve: g(g(-1))
plug -1 into g first, then plug that into x for g ANSWE::: -1
write the expression as a complex number in standard form (3+i)(10+7i)
since its multiplication, make a box. answer is 23+31i
how do you solve a problem like this: x^2 + y^2 + 4x - 18y + 69 = 0
solve by completing the square Step 1: group x's, add a box. group y's, add a box. = constant, plus two boxes Step 2: find #'s to complete the square. this is done by (b/2) squared. on the left side, fill in the boxes with the numbers that you put in for the boxes on the right Step 3: factor left, combine right the center will be whatever numbers you plug in for x and y to get zero, and the radius will be the square root of the number on the left for this problem, the answer would be (x+2) ^2 + (y-9)^2 = 16 center: (-2, 9) radius: 4
factor x^3 + 6x^2 +5x - 12 by x-1
synthetic divison to get x^2 + 7x + 12, then use calculator to factor it, to get (x+3)(x+4) then add the (x-1)
solve: √3x+10 = 8
take ^2 of both sides, solve for x ANSWER:: x=18
how would you solve the following problem? factor 2x^3 - 10x^2 + 12x
take a gif out, then work inside parenthesis. make a box for this problem, it would be 2x(x-3)(x-2)
the number under the radical is called...
the discriminant
how do you know how many solutions there will be to a polynomial?
the largest exponent tells you
how do you find axis of symmetry when graphing?
the line that is right in the middle of the parabola. if it is vertical, then it is x=. if it is horizontal, then it is y=
how do you find the solutions of a quadratic?
try to use calculator to factor, if it doesnt, then use quadratic formula
solve 3x^2-48
x= + or - 4
solve: -4 * 3√x+10 =3 =15
x= -37
simplify: x^8y^5 -------- x^5y^-5
x^3y
evaluate/simplify 6xy^3/4 --------- 3x^1/2y^1/2
xy^3/4 2 -------- x^1/2y^1/2
How would you solve the following equation? x^3-9x+8=0
you would find two numbers that multiply to equal 8 and add up to -9. Then write them in intercept form, then the numbers that you would plug in to make 0 would be your solutions The solutions for this problem would be 8 and 1, because two numbers that add up to -9 and multiply to 8 are -1 and -8. Written in intercept form, it would be (x-8) (x-1) the x's would be 8 and 1
how would you solve a problem like this: x^4 ---- ALL TO THE -3 y^-4
Distribute the -3, then put a 1 over x and y to the twelth
