6.18.T - Test: Module 6

Identify the factors of the expression 8a3 − 125.

(2a − 5)(4a2 + 10a + 25)

Identify the factors of the expression x3 + 4x2 −16x −64.

(x + 4)(x + 4)(x −4)

Multiply 2pq(3q − 4p).

6pq2 − 8p2q

Identify the simplest polynomial function with the given zeros.−1, −2, 3

P(x) = x3 − 7x − 6

Divide.

q − 4

Identify the binomial that is a factor of the polynomial P(x) = x3 − 5x2 − 2x + 24.

x+2

Solve the equation by factoring.4x4 − 20x3 − 96x2 = 0

−3, 0, 8

Solve by finding all roots.x4 + 4x3 + 4x2 + 4x + 3 = 0

−3, −1, i, −i

Factor.6ab − 15a − 8b + 20

(3a − 4)(2b − 5)

Find the factors of f(x) given that x = 4 is a zero.f(x) = x3 + x2 − 26x + 24.

(x − 4)(x − 1)(x + 6)

Evaluate h(x) = 2.8x3 + 0.01x2 − 1 for x = 1 and x = 2.

1.81; 21.44

Identify the standard form for and the leading coefficient of the polynomial.9h4 + 15h5 − 3h2 + 40

15h5 + 9h4 − 3h2 + 40The leading coefficient is 15.

Divide.(12p3 − 24p2 + 6p) ÷ 6p

2p2 − 4p + 1

Add.(28a2 − 10) + (5a2 − 2b + 6)

33a2 − 2b − 4

Which of the following represents the polynomial 5x + 3x4 + 15 − 7x3 in standard form, the degree of the polynomial, and the number of terms?

3x4 − 7x3 + 5x + 15degree: 4number of terms: 4

Multiply (4m + 2)(m2 − m + 1).

4m3 − 2m2 + 2m + 2

Graph f(x) = x3 + x2 − 4x + 2 on a calculator and estimate the correct local maximum and minimum.

6.88; −0.06

Subtract.(9a3 + 6a2 − a) − (a3 + 6a − 3)

8a3 + 6a2 − 7a + 3

Identify the simplest polynomial function having integer coefficients with the given zeros.

P(x) = x4 + 4x3 − 3x2 − 12x

The table shows the number of phones sold by a small cell phone provider in various years. Use a calculator to write a quartic model for the number of phones sold in a given year since 2000 and use the model to estimate the number of phones sold in 2010.

P(x) ≈ −0.44x4 + 11.85x3 − 108.66x2 + 415.64x − 75.33The estimated number of phones sold in 2010 is 665.

Identify the roots of the equation and the multiplicities of the roots.(x − 2)(x − 3)2 = 0

The root 2 has a multiplicity of 1. The root 3 has a multiplicity of 2.

Use finite differences to identify the degree of the polynomial that best describes the data. 1,7,13,19,25,31 3,-9,-18,- 21,-15,3

cubic

For f(x) = x3 − 10, identify the rule for g(x) = f(x − 2) + 16 and its graph.

g(x) = (x − 2)3 + 6 (The one that looks like an intersecting river or a infinity sign) Not the one that looks like a "X"

Let f(x) = −x3 − 8x2 − 9x + 11. Identify the function g that reflects f acrossthe y-axis.

g(x) = x3 − 8x2 + 9x + 11

Identify the correct leading coefficient, degree, and end behavior of P(x) = 6x4 + 3x3 − 2x − 7.

leading coefficient: 6degree: 4end behavior:as x → −∞, P(x) → +∞as x → +∞, P(x) → +∞