Polynomials Review EOC

Which choice is equivalent to the expression shown below?

48x³ - 243xy²

• 3(4x² - 9y)(4x² - 9y)

• 3(4x² - 9y)(4x² + 9y)

• 3(4x - 9y)(4x - 9y)

• 3(4x - 9y)(4x + 9y)

A polynomial, p(x) , has a lead coefficient of 1 and exactly three distinct zeros.

• x = -1 is a zero of multiplicity two
• x = 2 is a zero of multiplicity one
• x = 4 is a zero of multiplicity one

What choice shows p(x) ?

• p(x) = x³ - 5x² + 2x + 8

• p(x) = x³ + 5x² + 2x - 8

• p(x) = x⁴ - 4x³ - 3x² + 10x +8

• p(x) = x⁴ + 4x³ - 3x² - 10x +8

Which expression is equivalent to

(x² - 2x - 37) ÷ (x² - 3x - 40) ?

• 1 + x + 3

  x² - 3x - 40

• 1 - x + 3

  x² - 3x - 40

• 1 + 2x - 37

  x² - 3x - 40

• 1 + 2x - 37

  x² - 3x - 40

The graph of the function m(x) = x³ +3x² - 2x - 4 has a zero at -1. What are the other zeros of the function?

• -2 and 2

• -1 and 4

• -1 ± √5

• 1 ± 2√3

The function below, f(x), has (x - 7) and (x + 4) as factors,

f(x) = 2x⁵ - 13x⁴ + 22x³ - 187x² - 160x +336

What is the total number of real zeros of f(x) ?

• 2

• 3

• 4

• 5

What is the remainder when x³ - 1 is divided by (x + 2) ?

• 7

• 0

• -9

• -2

A function is shown below.

H(x) = 4x³ - 5x² - 23x + 6

What is the distance, to the nearest hundredth of a unit, between the two zeros that are closest to each other?

• 2

• 2.25

• 3

• 3.25