Deck 5: Section 1: Factoring

Question 1

Factor the given polynomial completely. If the polynomial is prime, say so. w² - 8w

A) The polynomial is prime.
B) w(w - 8)
C) w(w² - 8w)
D) (w - 8)(w + 8)

Answer 1

w(w - 8)

Question 2

Factor. 16r² - 25

A) The expression is prime.
B) (4r - 5)²
C) (4r - 5)(4r + 5)
D) (16r - 5)(16r + 5)

Answer 2

(4r - 5)(4r + 5)

Question 3

Factor. 125x³ - 27

A) (5x - 3)(25x² - 15x + 9)
B) (5x + 3)(25x² - 30x + 9)
C) (5x + 3)(25x² - 15x + 9)
D) (5x - 3)(25x² + 15x + 9)

Answer 3

(5x - 3)(25x² + 15x + 9)

Question 4

Factor out the opposite of the greatest common factor. 35y³ - 7y²

A) -7y²(5y - 1)
B) -7y²(-5y + 7)
C) -7y²(-5y + 1)
D) -y²(35y - 7)

Question 5

Factor. vw - 9w - 2v + 18

A) (v - 9)(w - 2)
B) The expression is prime.
C) (v + 9)(w + 2)
D) (v - 2)(w - 9)

Question 6

Find the prime factorization. 88

A) 8·11
B) 2²·3·11
C) 2³·11
D) 2·44

Question 7

Factor completely. 8w³x - 800wx

A) The expression is prime.
B) 8wx(w - 10)(w + 10)
C) 8wx(w - 10)²
D) 8wx(w² - 10²)

Question 8

Factor. qrs - 5q - 6rs + 30

A) (q - 6)(rs - 5)
B) (q + 6)(rs - 5)
C) The expression is prime.
D) (q - 5)(rs - 6)

Question 9

Factor. n² + 5np + 25p²

A) The polynomial is prime.
B) (n - 5p)(n + 5p)
C) (n + 5p)²
D) (n + p)(n + 5)

Question 10

Factor. 36u² - 12u + 1

A) The expression is prime.
B) (6u - 1)²
C) (6u - 1)(6u + 1)
D) (6u + 1)²

Question 11

Factor the given polynomial completely. If the polynomial is prime, say so. x³ + xy + 2x² + 2y

A) The polynomial is prime.
B) (x + 2)(x² + y)
C) (x + 2)(x + y)
D) (x² + 2)(x + y)

Question 12

Factor the given polynomial completely. 6v²w - 48vw + 90w

A) w(6v - 30)(6v - 18)
B) 6w(v - 5)(v - 3)
C) The polynomial is prime.
D) 6w(v² - 8v + 15)

Question 13

Factor completely. b³r³ - 12b²r² + 36br

A) br(br - 6)²
B) r(b³r - 6b²)
C) br(b²r² - 12br + 36)
D) br(br - 6)(br + 6)

Question 14

Factor out the greatest common factor. (m - 4)8 + (m - 4)m

A) The polynomial is prime.
B) m² + 4m - 32
C) (m - 4)8 + m
D) (m - 4)(8 + m)

Question 15

Find the greatest common factor for the given numbers. 9, 48

A) 6
B) 9
C) 1
D) 3

Question 16

Factor the given polynomial completely. If the polynomial is prime, say so. 5r² + 34r + 45

A) (5r - 9)(r + 5)
B) (5r - 9)(r - 5)
C) The polynomial is prime.
D) (5r + 9)(r + 5)

Question 17

Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial. n³ + 4n² - 9n - 36, n + 3

A) (n + 3)(n² - 7n - 12)
B) (n + 3)(n + 3)(n - 4)
C) (n + 3)(n² + n - 12)
D) (n + 3)(n - 3)(n + 4)

Question 18

Find the greatest common factor of the given terms. 6wx, 14xy, 10wy

A) 2wx
B) 1
C) 2wxy
D) 2

Question 19

Factor out the greatest common factor. 81s²t² - 63s²t + 54st²

A) -9s²t²(-9st + 7s - 6t)
B) st(81st - 63s + 54t)
C) The polynomial is prime.
D) -9st(-9st + 7s - 6t)

Question 20

Factor the given polynomial completely. c⁴ + d⁴

A) c²d²(c² - d²)
B) (c - d)²(c + d)²
C) The polynomial is prime.
D) (c - d)(c + d)(c² + d²)

Question 21

Solve the given equation. v³ - 3v² - 13v + 15 = 0

A) -3, 1, 5
B) 3, -1
C) 1, 5
D) 3, 1, -5

Question 22

Factor the given polynomial completely. z⁶ - 8z³ + 7

A) The polynomial is prime.
B) (z³ - 7)(z - 1)(z² - z - 1)
C) (z³ - 7)(z - 1)(z² + z + 1)
D) (z³ + 7)(z + 1)(z² + z + 1)

Question 23

Solve the equation.

A) 1, 5
B)
C)
D)

Question 24

Solve the given equation. w² = 8w

A) 8
B) 64
C) 0, 8
D) 8, -8

Question 25

Audrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t) = -16t² - 54t + 306. How many seconds elapse before the marble hits the ground?

A) 6 sec
B) 5 sec
C) 3 sec
D) 4 sec