Math Exam 2 Material
Factor the expression by grouping: 2x^3^ - 3x^2^ -12x +18
(2x - 3)(x^2^ -6)
Factor the difference of two squares: 25x^2^ - 64
(5x + 8)(5x - 8)
Factor the trinomial, or state that the trinomial is prime: 2a^2 + 7ab + 5b^2
(a + b)(2a + 5b)
Factor the following expression completely: u^2n^ + 12u^n^ + 27
(u^n^ + 3)(u^n^ + 9)
Factor out the greatest common factor: x(x + 3) - 17(x + 3)
(x + 3)(x - 17)
Factor the following by grouping: x^2^ + 3x - 7x -21
(x + 3)(x - 7)
Factor the difference of two squares: x^2^ - 16
(x + 4)(x - 4)
Factor by introducing an appropriate substitution: 3x^4^ - 4x^2^ - 20
(x^2^ + 2)(3x^2^ - 10)
Simply the following complex rational expression: x/9 - 1 / x-9
1/9, x does not = 9
Simplify the exponential expression: (-2x^5^y)(-6x^4^y^12^)
12x^9^y^13^
Multiply: 4a^2^(5a^3^ + 11)
20a^5^ + 44a^2^ (Multiply variables, add exponents.)
Simplify the exponential expression: (5x^8^)(4x^4^)
20x^12^ (Multiply the variables, add exponents.)
Factor completely, or state that the polynomial is prime: 2x^3^ - 50x
2x(x + 5)(x - 5)
Factor the trinomial completely: 3x^2^ + 24x + 45
3(x + 3)(x + 5)
Multiply (Simplify your answer.): 6x^3^y(7x^3^ - x^4^y^2^ + 6y^2^)
42x^6^y - 6x^7^y^3^ + 36x^3^y^3^
Perform the indicated operation and simplify the result: 4 + 1/x / 7 - 1/x
4x + 1 / 7x - 1, x does not = 0, 1/7
Perform the indicated computation. Write the answer in scientific notation: (2 x 10^5^)(2.7 x 10^3^)
5.4 x 10^8^ (Multiply the stand alone variables, leave the variables attached to x, add the exponents.)
What is the first step to solve this equation? 6/x + 2/5 = 8/x
5x
Simplify the expression: 45x^9^ / 9x^3^
5x^6^ (Divide the variables, subtract the exponents.)
Find the degree of the polynomial: 5x^6^ + 9x^2^ + 4
6 (The degree is the largest exponent on the variable.)
Write the polynomial in standard form and indicate its degree: (5x^2^ - 8x -1) + (2x^2^ -3x + 7) - (x^2^ - 5x -4) =
6x^2^ - 6x + 10 Degree= 2
The zero-product principle states that if AB = 0, then ...
A = 0 or B = 0
A simplified polynomial that has exactly two terms is called a....
Binomial
The set of real numbers for which a rational expression is defined is the ... of the expression
Domain
A simplified polynomial that has exactly one term is called a...
Monomial
An equation that can be written in the general form ax^2^ + bx + c = 0, a ≠ 0 is called a ... equation.
Quadratic
If a does not equal 0, the degree of ax^n^ is ...
The degree of each term is the value of the exponent, so, the degree is n.
Solve the equation by factoring: 2x(x-3) = 7x^2^ - 7x
The solution set is {0, 1/5}
Solve the equation by factoring: 8x^2^ + 10x - 7 = 0
The solution set is {1/2, -7/4}
Solve the equation by factoring: x^2^ = 5x + 24
The solution set is {8, -3} (Factor and set each factor equal to zero.)
The rule for the square of a binomial is...
The square of a binomial difference is equal to the first term squared, minus 2 times the product of the terms, plus the last term squared. (A-B)^2^ = A^2^ - 2AB + B^2^
Find all integers b so that so that the following trinomial can be factored: y^2^ + by + 8
The values of b are 6, -6 ,9, -9 (ay^2^+by+c, u+v=b, uv=ac)
A simplified polynomial that has exactly three terms is called a...
Trinomial
One must exclude all numbers from this set that make the denominator of the rational expression ...
Zero
Factor out the GCF from the polynomial: a^4^b^6^ - a^3^b^2^ + a^2^b^5^ - a^2^b^2^
a^2^b^2^ (a^2^b^4^ - a + b^3^ - 1)
A rational expression whose numerator or denominator or both contains rational expressions is called a/an ... rational expression or a/an ... fraction.
complex; complex
Simplify the following complex rational expression: x - 8 / x - 8/x-7
x - 7 / x + 1, x does not = -1, 7, 8
Simplify the complex rational expression: 1/x+1 / 1/x^2^-x-2 + 1/x-2
x-2 / x+2, x does not = -1, 2, -2
Write the polynomial in standard form: (-4x^3^ + 7x^2^ - 10x + 3) + (3x^3^ + 10x^2^ - 5x - 5) =
−x^3^ + 17x^2^ − 15x − 2