MAT 120
Homework 6
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Multiply.
1) 3x5 (-3x2 + 12)
A) 27x5
B) -9x7 + 12
C) -9x2 + 36
2) (x + 2y)(x + 9y)
A) x2 + 11xy + 18y2
C) x2 + 8xy + 18y2
B) x + 11xy + 18y
D) x2 + 11xy + 11y2
B) 5y4 - 10y3 - 5y2 + 11y - 3
3)
D) 5y4 - 5y3 - 5y2 + 11y - 3
C) 5y4 - 5y3 - 8y2 + 11y - 3
4) ( 13 m - 9 w)( 13 m + 9 w)
A) 13 m2 - 9 w2
C) 169 m 2 + 234 mw - 81 w2
B) 169 m 2 - 234 mw - 81 w2
D) 169 m 2 - 81 w2
Solve the problem.
5) Find and simplify f(k - 1), given f(x) = 4x2 + 2x - 1.
A) f(k - 1) = -6k2 + 4k + 1
B) f(k - 1) = 4k2 - 6k + 1
D) f(k - 1) = 4k2 - 2k + 5
C) f(k - 1) = 4k2 - 6k + 5
6) b5 - 29by4 + 17b3 y8 - 3b5 y4
4)
5)
6)
A) by4 (b4 - 29 + 17b2 y4 - 3b4 )
B) b2 (b4 - 29y3 + 17b2 y7 - 3b4 y3 )
C) by(b4 - 29y3 + 17b2 y7 - 3b4 y3 )
D) b(b4 - 29y4 + 17b2 y8 - 3b4 y4)
Factor out a factor with a negative coefficient.
7) -2x2 + 4x - 56
A) 2(x2 - 2x + 28)
B) -2(x2 - 2x + 28)
D) -2(-x2 - 2x + 28)
C) 2(-x2 - 2x + 28)
Solve.
1)
2)
3) (5y2 + 5y - 3)(y2 - 2y + 1)
A) 5y4 - 10y3 - 8y2 + 11y - 3
Factor.
D) -9x7 + 36x5
8) The growth of revenue R(t) over a 12-year time period for Acme Computer Products is given by
R(t) = 0.7t + 42t2 thousand dollars, where t = time in years. Find an equivalent expression for R(t)
by factoring out a common factor.
A) 7t(0.1 + 6t)
B) -7t(0.1 - 6t)
C) 6t(0.1 + 7t)
D) 42(0.1t + t2 )
1
7)
8)
Factor.
9) 5m(3 - m) + 9n(3 - m)
A) No common factor
C) (5m - 9n)(3 - m)
10) x3 - 7x 2 - 8x + 56
A) (x - 7)(x2 + 8x)
B) (x - 7)(x2 - 8)
C) (x + 7)(x2 + 8)
D) (x + 7)(x3 - 8)
11) x2 + 10x - 24
A) (x - 12)(x + 2)
B) (x + 12)(x - 2)
C) (x - 12)(x + 1)
D) Not factorable
12) u2 - 2uv - 8v2
A) (u - 2v)(u + v)
B) (u + 2v)(u - 4v)
C) (u - v)(u + 4v)
D) (u - 2v)(u + 4v)
2
1
13) y2 - y +
5
25
1 2
A) y 5
14) x3 - x2 - 72x
A) x(x + 8)(x - 9)
10)
11)
12)
13)
B) y y -
2
5
C) y +
1 2
5
D) Not factorable
14)
B) (x2 + 1)(x - 72)
C) x(x + 9)(x - 8)
D) Not factorable
15) x8 - 6x 4 - 55
A) (x4 - 5)(x4 + 1)
B) (x4 + 5)(x4 - 11)
C) (x4 - 5)(x4 + 11)
D) Not factorable
16) 5x2 - 38x - 16
A) (2x + 5)(x - 8)
B) (5x + 2)(x - 8)
C) (x - 2)(x - 8)
D) (x + 5)(x - 8)
17) 6x2 + 26x - 20
A) 2(3x + 2)(x - 5)
B) (3x - 2)(2x + 10)
C) 2(3x - 2)(x + 5)
D) (6x - 4)(x + 5)
18) 8z 2 - 6zy - 9y2
A) (2z - 3y)(4z + 3y)
C) (8z + y)(z - 9y)
15)
B) (8z - 3y)(z + 3y)
D) (2z + 3y)(4z - 3y)
19) 9y4 - 9y2 - 10
A) (3y2 + 1)(3y2 - 10)
B) (9y2 - 5)(y2 + 2)
D) (3y2 - 5)(3y2 + 2)
C) (3y - 2)(3y + 5)
Solve.
9)
B) (5m + 9n)(3 - m)
D) m(5 + 9n)(3 - 1)
20) Pet-Me-Some-More Pet Supplies determines it will sell S(x) = 5000 - 500x + 100x2 - 5x3 gourmet
dog biscuits in one week if it sells them for x cents each. Find an equivalent expression for the
trinomial S(x) - 5000 by factoring.
A) -5x(x - 10)(x + 10)
B) 5x(x - 10)2
C) -5x(x - 10)2
D) -5x(x + 10)2
2
16)
17)
18)
19)
20)