UNIT TEST: MATH

7 September 2022
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question
If (x + k) is a factor of f(x), which of the following must be true?
answer
f(-k) = 0
question
Which statement best describes the equation x5 + x3 - 14 = 0?
answer
The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.
question
Which statement about 4x2 + 19x - 5 is true?
answer
One of the factors is (x + 5).
question
Logan saves the same amount of money each month for college. His current total savings is 300m2 + 120m + 180 dollars. Which factorization could represent the number of months and amount of a monthly deposit in dollars?
answer
60(5m2 +2m +3)
question
What are the solutions of the equation (x + 2)2 + 12(x + 2) - 14 = 0? Use u substitution and the quadratic formula to solve.
answer
x=-8+-5 square root of 2
question
According to the Rational Root Theorem, which could be a factor of the polynomial f(x) = 60x4 + 86x3 - 46x2 - 43x + 8?
answer
6x - 1
question
What is the end behavior of the graph of the polynomial function f(x) = -x5 + 9x4 - 18x3?
answer
As *X -> NEGATIVE* infinite sign, *Y -> POSITIVE* infinite sign and as *X -> POSITIVE* infinite sign, *Y -> NEGATIVE* infinite sign.
question
The polynomial function f(x) = 3x5 - 2x2 + 7x models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level. Which answer choice represents all potential values of when the roller coaster is at ground level? Begin by factoring x to create a constant term.
answer
0, +- 1/3, +-1, +-7/3, +-7
question
Anja divides (8x3 - 36x2 + 54x - 27) by (2x - 3) as shown below. What error does Anja make?
answer
She makes a multiplication error.
question
Arpitha factors out the greatest common factor, 9n, from the terms of the polynomial shown. 162m3n4 + 45n = 9n(_______ + 5)
answer
18m3n3
question
The area of a rectangle is (x3 - 5x2 + 3x - 15), and the width of the rectangle is (x2 + 3). If area = length Ɨ width, what is the length of the rectangle?
answer
x - 5
question
What are the solutions of the equation (x + 2)2 - 2(x + 2) - 15 = 0? Use u substitution to solve.
answer
x = -5 and x = 3
question
What are the solutions of the equation x4 - 5x2 - 36 = 0? Use factoring to solve.
answer
x= +-2i and x= +-3
question
What is the product? (5r āˆ’ 4)(r2 āˆ’ 6r + 4)
answer
5r3 āˆ’ 34r2 + 44r āˆ’ 16
question
What is the completely factored form of 9x2 + 24x + 16?
answer
(3x + 4)(3x + 4)