Factor the trinomial, or state that the trinomial is prime.
339)
x2+ 6x – 27
339)
A)
(x + 9)(x – 3)
B)
(x – 9)(x + 1)
C)
prime
D)
(x – 9)(x + 3)
Factor the trinomial by grouping, or state that the trinomial is prime.
340)
12x2+ 25xy + 12y2
340)
A)
(12x + 3y)(x + 4y)
B)
prime
C)
(4x + 3y)(3x + 4y)
D)
(4x – 3y)(3x – 4y)
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
341)
2x2+17x –21
341)
A)
prime
B)
(2x +3)(x –7)
C)
(2x –3)(x +7)
D)
(2x –7)(x +3)
Multiply the monomials. Assume any variable exponents represent whole numbers.
342)
(2x7y)(–4x3y6)
342)
A)
–2x21y6
B)
–2x10y7
C)
–8x10y7
D)
–8x10y6
Factor by introducing an appropriate substitution.
343)
3y6–34y3+40
343)
A)
y4(3y –4)(y –10)
B)
(3y3–4)(y3–10)
C)
y2(3y2–4)(y2–10)
D)
(3y3–10y2+ y –4)(y3–4y2+ y –10)
81
A
Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
344)
(11x – y)(8x –6y)
344)
A)
88x2–74xy +6y2
B)
19x2–74xy +6y2
C)
88x2+74xy +6y2
D)
88x2–74xy –6y2
345)
(x + 6)(x – 11)
345)
A)
x2– 5x – 66
B)
x2– 5x – 5
C)
x2– 66x – 5
D)
x2– 6x – 66
Factor the trinomial by grouping, or state that the trinomial is prime.
346)
2a2+ 9ab –35b2
346)
A)
(2a –5b)(a +7b)
B)
(2a +5b)(a –7b)
C)
(2a +7b)(a –5b)
D)
prime
Perform the indicated operations.
347)
(8x2+ 8x – 2) – (–7x2+ 4x – 8)
347)
A)
15x2– 4x – 6
B)
15x2+ 4x + 6
C)
15x2– 4x + 6
D)
15x2+ 4x – 6
Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
348)
(x –7y)(5x –6y)
348)
A)
5x2–41xy +13y2
B)
5x2–41xy +42y2
C)
5x2–41xy –42y2
D)
5x2+41xy +42y2
A
Factor by introducing an appropriate substitution.
349)
x4–10x2+16
349)
A)
(x2–8)(x2–2)
B)
(x4+8)(x4+2)
C)
(x2– x +8)(x2+ x +2)
D)
(x2–8x +8)(x2–2x +2)
Factor by grouping. Assume any variable exponents represent whole numbers.
350)
xnyn– 2xn+ 7yn– 14
350)
A)
(yn+ 2)(xn+ 7)
B)
(yn– 2)(xn+ 7)
C)
(yn+ 7)(xn– 2)
D)
(yn+ 7)(xn+ 2)
Factor by introducing an appropriate substitution.
351)
5y10 – 23y5–42
351)
A)
(5y5+6y3+7)(y5–7y3–6)
B)
(5y5–7)(y5+6)
C)
(5y5+7)(y5–6)
D)
y8(5y +7)(y –6)
Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
352)
(9x2+5y)2
352)
A)
81x4+106x2y +25y2
B)
81x4+90x2y +25y2
C)
81x2+90x2y +25y2
D)
81x4+45x2y +25y2
Factor completely, or state that the polynomial is prime.
353)
x4–18x2y2+81y4
353)
A)
(x2–3y2)2
B)
(x +3y)2(x –3y)2
C)
(x +3y)4
D)
(x –3y)4
83
Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
354)
(7x + 5)(8x + 6)
354)
A)
15x2+ 82x + 30
B)
56x2+ 82x + 82
C)
56x2+ 82x + 30
D)
15x2+ 82x + 82
Factor by grouping. Assume any variable exponents represent whole numbers.
355)
ax2– 4ax + 8a – bx2+ 4bx – 8b
355)
A)
(x2– 4x + 8)(a + b)
B)
(x2+ 4x – 8)(b – a)
C)
(x2+ 4x – 8)(a – b)
D)
(x2– 4x + 8)(a – b)
Factor any perfect square trinomial, or state that the polynomial is prime.
356)
x2– 12xy + 144y2
356)
A)
(x + 12)2
B)
prime
C)
(x + 12)(x – 12)
D)
(x – 12)2
Use factoring to solve the polynomial equation.
357)
4x3+3x2=36x +27
357)
A)
{–3, 3}
B)
–3, –3
4, 3
C)
–3
4, 0
D)
–3
4, 3
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
358)
(2x – y + 4z)(2x – y – 4z)
358)
A)
4x2– 4xy + y2+ 16xz + 8yz – 16z2
B)
4x2+ y2+ 16xz + 8yz – 16z2
C)
4x2+ y2– 16z2
D)
4x2– 4xy + y2– 16z2
84
C
Factor completely, or state that the trinomial is prime.
359)
12y5– 7y4– 12y3
359)
A)
y3(3y + 4)(4y – 3)
B)
y3(12y – 4)(y + 3)
C)
y3(3y – 4)(4y + 3)
D)
prime
Factor by grouping. Assume any variable exponents represent whole numbers.
360)
18x2+ 12xy + 15xy + 10y2
360)
A)
(6x – 5y)(3x + 2y)
B)
(6x + 5)(3x + 2)
C)
(18x + 5y)(x + 2y)
D)
(6x + 5y)(3x + 2y)
Use factoring to solve the polynomial equation.
361)
5x4–180x2= 0
361)
A)
{–6 5, 0, 6 5}
B)
{0}
C)
{–6, 6}
D)
{–6, 0, 6}
Use factoring to solve the quadratic equation.
362)
4x(x – 4) = (3x – 6)(x – 4)
362)
A)
{4, –6}
B)
{–6}
C)
{–4, 6}
D)
{6}
Perform the indicated operations.
363)
(4x – 3y)(4x + 3y)
363)
A)
16x2– 9y2
B)
16x2– 24xy – 9y2
C)
4x2– 3y2
D)
16x2+ 24xy – 9y2
85
C
Add the polynomials. Assume all variable exponents represent whole numbers.
364)
(3x2n –xn– 1) + (x2n +4xn+3)
364)
A)
3x2n +4xn+3
B)
4x2n +3xn+2
C)
2x4n – 5x2n – 4
D)
4x4n +5x2n +4
Factor completely, or state that the polynomial is prime.
365)
25x2– 90x + 81
365)
A)
(5x – 9)2
B)
(5x + 9)2
C)
prime
D)
(5x – 9)(5x + 9)
Subtract the polynomials. Assume all variable exponents represent whole numbers.
366)
(6x4y2+2x3y +3y) – (4x4y2+11x3y +8y +12x)
366)
A)
2x4y2– 9x3y – 5y +12x
B)
10x4y2+ 13x3y + 11y +12x
C)
2x4y2– 9x3y – 5y – 12x
D)
2x4y2+ 9x3y – 5y – 12x
Perform the indicated operations.
367)
Let f(x) = x – 3 and g(x) =4x + 9. Find (fg)(x) and (fg)(–2).
367)
A)
(fg)(x) =4x2+ 3x – 27; (fg)(–2) = – 5
B)
(fg)(x) =4x2– 3x + 27; (fg)(–2) =37
C)
(fg)(x) =4x2– 3x – 27; (fg)(–2) = – 25
D)
(fg)(x) =4x2– 3x – 27; (fg)(–2) = – 5
Factor completely, or state that the trinomial is prime.
368)
24x2y –34xy2+12y3
368)
A)
2y(3x – y)(4x –6y)
B)
2y(3x +2y)(4x +3y)
C)
2y(3x –2y)(4x –3y)
D)
prime
86
Find the product. Assume all variable exponents represent whole numbers.
369)
(xy –12)(x2y2+8xy +10)
369)
A)
x3y3+ 8x2y2+ 10xy
B)
x3y3+ 20x2y2+ 106xy + 120
C)
x3y3– 4x2y2– 86xy – 120
D)
12x3y3– 96x2y2– 120xy
Factor by grouping. Assume any variable exponents represent whole numbers.
370)
ax –bx +by –ay
370)
A)
(a +b)(x+y)
B)
(a +b)(x–y)
C)
(a –b)(x+y)
D)
(a –b)(x–y)
Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
371)
12x4–8x2
371)
A)
4x2(3x2–2)
B)
4(3x4–2x2)
C)
4x2(3x3–2)
D)
x2(12x2–8)
Factor by grouping to obtain the difference of two squares.
372)
x3+5x2–16x –80
372)
A)
(x +5)(x –4)2
B)
(x +5)(x +4)(x –4)
C)
(x +5)(x2–16)
D)
(x –5)(x +4)(x –4)
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
373)
7x2– x – 8
373)
A)
(7x + 1)(x – 8)
B)
(7x + 8)(x – 1)
C)
(7x – 8)(x + 1)
D)
(7x – 1)(x + 8)
C
Find the indicated function value.
374)
Find f(–4) when f(x) =3x2+ 2x – 7.
374)
A)
47
B)
1
C)
49
D)
33
Factor completely, or state that the polynomial is prime.
375)
(c + d)4–16
375)
A)
(c2+ 2cd +d2+4)(c + d +2)(c + d –2)
B)
(c2+ 2cd +d2+4)(c2+ 2cd +d2–4)
C)
(c + d +2)2(c + d –2)2
D)
prime
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
376)
5x2+ 7x + 6
376)
A)
(5x – 3)(x + 2)
B)
(5x + 2)(x – 3)
C)
prime
D)
(5x + 3)(x – 2)
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
377)
(4x + 5y)(4x – 5y)
377)
A)
16x2+ 40xy – 25y2
B)
16x2– 40xy – 25y2
C)
16x2– 25y2
D)
4x2– 5y2
Factor completely, or state that the polynomial is prime.
378)
48x2–68x +24
378)
A)
4(4x – 1)(3x –6)
B)
prime
C)
4x(6x –3)(x –2)
D)
4(4x –3)(3x –2)
88
D
Solve the problem.
379)
Write a polynomial that represents the volume of the open box.
x
11 –5x
2–5x
379)
A)
22 –65x +25x2
B)
22x –65x2+5x3
C)
22x +65x2+25x3
D)
22x –65x2+25x3
380)
The length of a rectangular storage room is 5 feet longer than its width. If the room’s area is 84
square feet, find its length and width.
380)
A)
width: 6 ft, length: 11 ft
B)
width: 6 ft, length: 13 ft
C)
width: 8 ft, length: 13 ft
D)
width: 7 ft, length: 12 ft
381)
Researchers conducted a weight loss study of moderately overweight women. In addition to
dieting, the women kept exercise and weight loss journals for one year. The researchers used this
data to derive a polynomial function that models average monthly weight loss as a function of
average weekly minutes of aerobic exercise. As its coefficients make the function difficult to
compute by hand, the graph below was used in estimating.
Use the graph to estimate the average number of minutes a woman exercised per week if her
average monthly weight loss was 6.1 pounds.
381)
A)
165 min
B)
157 min
C)
150 min
D)
145 min
Find the product. Assume all variable exponents represent whole numbers.
382)
(x +6)(7x2+8x +3)
382)
A)
7x3+50x2+51x +18
B)
336x4+7x3+144x2+18
C)
49x3+56x2+21x
D)
7x3+42x2+48x +18
Solve the polynomial equation.
383)
x3+8x2– x –8= 0
383)
A)
{64}
B)
{–1, 1, –8}
C)
{–8, 8}
D)
{1, –8, 8}
90
Use factoring to solve the quadratic equation.
384)
x(3x +16) =12
384)
A)
2
3,–6
B)
3
2, 6
C)
0, 16
3
D)
0, –16
3
385)
x2–16 =15x
385)
A)
{1, –16}
B)
{–1, 16}
C)
{–4, 4}
D)
{–4, –4}
Factor completely, or state that the polynomial is prime.
386)
4x4–36x2
386)
A)
4(x2+3)(x2–3)
B)
4x2(x +3)(x –3)
C)
4(x2+3x)(x2–3x)
D)
prime
Use factoring to solve the quadratic equation.
387)
x2=4x
387)
A)
{0}
B)
{–4, 0}
C)
{0, 4}
D)
{0, 2}
Factor the trinomial, or state that the trinomial is prime.
388)
x2– x – 42
388)
A)
(x + 7)(x – 6)
B)
prime
C)
(x + 1)(x – 13)
D)
(x + 6)(x – 7)