ACE College Algebra II - Unit 7 Review

If -3x³+5x²-2 is divided by (x-2), what is the remainder?

• -4

• -6

• 42

• 0

Tags

CCSS.HSA.APR.B.2

Find the value of k so that the binomial (x + 2) is a factor of the function f(x) = 2x³ - 3x² + kx – 6.

• -15

• 14

• -17

• 17

Tags

CCSS.HSA.APR.B.2

Simplify the given expression using the properties of exponents.

• 
• 
• 
• 

Tags

CCSS.8.EE.A.1

In standard form, (3x + 1)(x² + 3x - 3) – (x + 2)² simplifies to

• 3x³ + 6x² - 3x

• 3x³ + 8x² - 11x + 1

• 3x³ + 8x² - 3x + 1

• 3x³ + 6x² - 11x – 7

Tags

CCSS.6.EE.A.3

Which of the following polynomials is/are correctly factored?

I. 2x³ + 3x² – 8x - 12 = (2x + 3)(x² + 4)

II. 16c⁴ – 9d² = (4c² + 3d)(4c² – 3d)

III. 64a³ - 27 = (4a - 3)(16a² + 12a + 3)

• I and II only

• I, II and III

• II only

• II and III

Tags

CCSS.HSA.APR.C.4

A quintic function, g(x), is such that its leading coefficient is −2. Which two of the following would describe the correct end behaviors of the graph of the function?

I. As x → −∞, g(x) → −∞. II. As x → −∞, g(x) → ∞.

III. As x → ∞, g(x) → −∞. IV. As x → ∞, g(x) → ∞.

• I and IV

• I and II

• II and III

• II and IV

The graph of a polynomial function, q(x), is pictured here. Which of the following equations would be the standard form of q(x)?

• q(x) = -x⁴ - 3x² - 2x

• q(x) = -x⁴ - x³+ 3x² - 2x

• q(x) = -x⁴ + 3x² - 2x+1

• q(x) = -x⁴ + 3x² - 2x

Tags

CCSS.HSA.APR.B.3

If h(x) = (x + 3)³(x² - 6x + 9), what is the multiplicity of the zero x = 3?

• 1

• 2

• 3

• x = 3 is not a zero of g(x)

Tags

CCSS.HSF-IF.C.7C

Pictured here is the graph of the function

f(x) = ax⁷ + bx⁶ + cx⁴ + 4x³ + 3x² – 4x + d.

Which of the following statements is/are true?

I. The value of a > 0.

II. The factor (x+5) is a factor of f(x) that occurs twice.

III. The value of d is 2.

• I, II and III

• I only

• I and II only

• II only

Which of the following statements is NOT true about the function p(x) = 3x³ - 5x² – 2x ?

• The graph of p(x) passes through the origin.

• The graph of p(x) rises to the left and falls to the right.

• x = 0 is a root of p(x).

• The range of p(x) is (-∞, ∞).