Add the polynomials. Assume all variable exponents represent whole numbers.
162)
(2y2n – 3yn+ 6) + (7y2n + 9yn+ 9)
162)
A)
9y2n + 6yn+ 15
B)
9y4n + 6y2n + 15
C)
30y3n
D)
13y2n + 11yn+ 6
Factor completely, or state that the polynomial is prime.
163)
98x3– 56x2y + 8xy2
163)
A)
2x(7x – 2y)(7x + 2y)
B)
2x(7x + 2y)2
C)
prime
D)
2x(7x – 2y)2
Solve the problem.
164)
The floor of a rectangular storage room is divided into two right triangles by drawing a diagonal.
One leg of the resulting triangle, the width of the room, is 4 feet more than two times the other leg,
the length of the room. The hypotenuse is 26 feet. Find the length and the width of the room.
164)
A)
length: 11 ft, width: 26 ft
B)
length: 11 ft, width: 15 ft
C)
length: 10 ft, width: 14 ft
D)
length: 10 ft, width: 24 ft
165)
A department store is having a clearance sale. The price on a television is reduced by 22%. That sale
price is then reduced by another 22%. If x is the television’s original price, the sale price can be
represented by (x –0.22x) –0.22(x –0.22x). With these two reductions, at what percentage of the
original price is the television being sold? Use the factored, simplified form of the expression to
answer the question.
165)
A)
60.84%
B)
44%
C)
56%
D)
78%
Factor completely, or state that the polynomial is prime.
166)
y3– 12y2+ 144y
166)
A)
y(y + 12)2
B)
y(y2– 12y + 144)
C)
y(y – 12)2
D)
prime
167)
x2(a – b) +144(b – a)
167)
A)
(a – b)(x2+144)
B)
prime
C)
(a – b)(x +12)(x –12)
D)
(b – a)(x +12)(x –12)
C
Factor any difference of two squares, or state that the polynomial is prime. Assume any variable exponents represent
whole numbers.
168)
9x4– 49y6
168)
A)
(3x2– 7y3)2
B)
(3x2+ 7y3)2
C)
prime
D)
(3x2+ 7y3)(3x2– 7y3)
D
Find the indicated function value.
169)
Find f(2) when f(x) = x3+ 4x2+ 3x.
169)
A)
18
B)
14
C)
–18
D)
30
D
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
170)
(3x –9y +10)(3x –9y –10)
170)
A)
6x2+18y2–20
B)
3x2–27y2+9y2–10
C)
9x2+81y2–100
D)
9x2–54xy +81y2–100
D
42
B
Factor out the negative of the greatest common factor. Assume any variable exponents represent whole numbers.
171)
–40x3n +16x2n
171)
A)
–8x2n(5xn–2x)
B)
–8x2n(5xn–2)
C)
–8x3n(5xn–2)
D)
–8x2n(5xn+2)
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
172)
7x2+8xy +y2
172)
A)
(7x + y)(x +7y)
B)
(7x – y)(x – y)
C)
prime
D)
(7x + y)(x + y)
Subtract the polynomials. Assume all variable exponents represent whole numbers.
173)
(x3+6xy –9y2) – (4x3+9xy +y2)
173)
A)
3x3+ 3xy – 8y2
B)
–3x3– 3xy – 8y2
C)
–3x3– 3xy – 10y2
D)
5x3– 3xy – 10y2
Solve the problem.
174)
A rocket is stopped 20 feet from a satellite when it begins accelerating away from the satellite at a
constant rate of 18 feet per second per second. The distance between the rocket and the satellite is
given by the polynomial P(t) =9t2+20. Find the distance between the rocket and the satellite 11
seconds after the rocket started moving.
174)
A)
1109 ft
B)
119 ft
C)
141 ft
D)
1089 ft
Factor by introducing an appropriate substitution.
175)
x4– 9x2+ 14
175)
A)
(x2– 7)(x2– 2)
B)
(x2+ 7)(x2+ 2)
C)
(x2+ 7)(x2– 2)
D)
(x2– 7)(x2+ 2)
43
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
176)
(x + 12)(x – 12)
176)
A)
x2+ 24x – 144
B)
x2– 144
C)
x2– 24
D)
x2– 24x – 144
Factor completely, or state that the polynomial is prime.
177)
48x2y + 138xy –18y
177)
A)
6y(8x –1)(x +3)
B)
6y(8x +1)(x –3)
C)
prime
D)
6y(8x –1)(x –3)
178)
3x3+ 8x + 12x2+ 32
178)
A)
(x + 4)(3x2+ 8)
B)
(x + 4)(3x2– 8)
C)
(x + 4)(3x + 8)
D)
(x – 4)(3x2+ 8)
179)
343x3y3–x6y6
179)
A)
x3y3(7 – xy)(49 + 7xy +x2y2)
B)
x3y3(7 + xy)(49 – 7xy +x2y2)
C)
(7xy –x2y2)(49x2y2+ 7x3y3+x4y4)
D)
prime
Factor out the negative of the greatest common factor. Assume any variable exponents represent whole numbers.
180)
–5x – 15
180)
A)
–5(x – 3)
B)
–5(x + 3)
C)
5(x + 3)
D)
5(x – 3)
Add the polynomials. Assume all variable exponents represent whole numbers.
181)
(–2x6+ 12x4– 12) + (7x6+ 14x4– 2)
181)
A)
5x6+ 26x4– 14
B)
17x10
C)
5x6+ 26x4+ 10
D)
5x6+ 16x4+ 10
Factor any perfect square trinomial, or state that the polynomial is prime.
182)
x2+ 14xy + 49y2
182)
A)
(x + 7y)(x – 7y)
B)
(x – 7y)2
C)
(x + 7y)2
D)
prime
C
Factor completely, or state that the polynomial is prime.
183)
x8–y8
183)
A)
prime
B)
(x6+y6)(x3+y3)(x3–y3)
C)
(x4+y4)(x2+y2)(x + y)(x – y)
D)
(x6+y6)(x4+y4)(x2+y2)(x + y)(x – y)
C
Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
184)
21xy +35xz –14xw
184)
A)
x(21xy +35xz –14xw)
B)
7(3xy +5xz –2xw)
C)
7x(3y +5z –2w)
D)
x(21y +35z –14w)
C
Perform the indicated operations.
185)
(x + y)(x2– 8xy –y2)
185)
A)
x3– 8x2y – xy2
B)
x3y – 8x2y – xy3
C)
x3– 8x2y – 8xy2–y3
D)
x3– 7x2y – 9xy2–y3
D
45
A
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
186)
10x2+ 7x – 12
186)
A)
(2x + 3)(5x – 4)
B)
prime
C)
(2x – 3)(5x + 4)
D)
(10x + 3)(x – 4)
Give the degree and the leading coefficient of the polynomial.
187)
7x – 35 – 15x2–3x3
187)
A)
degree: 3; leading coefficient: 3
B)
degree: 3; leading coefficient: 7
C)
degree: 3; leading coefficient: –3
D)
degree: 2; leading coefficient: –15
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
188)
7x2– 20x – 3
188)
A)
(7x + 1)(x – 3)
B)
(7x – 1)(x + 3)
C)
(7x – 3)(x + 1)
D)
prime
Find the indicated function value.
189)
Find f(2) when f(x) =x2+ 4x – 3.
189)
A)
–7
B)
9
C)
15
D)
–1
Factor any perfect square trinomial, or state that the polynomial is prime.
190)
x2– 16x + 64
190)
A)
prime
B)
(x – 8)(x + 8)
C)
(x – 8)2
D)
(x + 8)2
46
Factor out the negative of the greatest common factor. Assume any variable exponents represent whole numbers.
191)
–8x2+16y
191)
A)
–8(x2–2y)
B)
–8(x2+2y)
C)
–8x(x –2y)
D)
–8x(x +2y)
Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
192)
–12x2y(–6x2y4– 11xy3– 10)
192)
A)
72x4y5+ 132x3y4+ 120
B)
72x2y5+ 132x3y4+ 120x2y
C)
72x4y5– 132x3y4– 120x2y
D)
72x4y5+ 132x3y4+ 120x2y
Factor completely, or state that the polynomial is prime.
193)
12x2+ 25x + 12
193)
A)
(4x + 3)(3x + 4)
B)
(12x + 3)(x + 4)
C)
(4x – 3)(3x – 4)
D)
prime
Use factoring to solve the polynomial equation.
194)
x3+8x2– x –8= 0
194)
A)
{64}
B)
{–8, 8}
C)
{–1, 1, –8}
D)
{1, –8, 8}
Factor any difference of two squares, or state that the polynomial is prime. Assume any variable exponents represent
whole numbers.
195)
49x2– 64
195)
A)
(7x + 8)(7x – 8)
B)
(7x + 8)2
C)
(7x – 8)2
D)
prime
Factor completely, or state that the polynomial is prime.
196)
28a2b + 204ab –160b
196)
A)
prime
B)
4(7a –5)(a –8)
C)
4b(7a –5)(a +8)
D)
4(7a +5)(a –8)
Factor by introducing an appropriate substitution.
197)
11(x + 3)2+ 13(x + 3) + 2
197)
A)
(11x + 5)(x + 4)
B)
(11x + 34)(x + 5)
C)
(11x + 35)(x + 4)
D)
(11x + 4)(x + 5)
C
Factor completely, or state that the polynomial is prime. Assume any variable exponents represent whole numbers.
198)
a3b2–100ac2
198)
A)
a(b +10c)(b –10c)
B)
a(ab +10c)(ab –10c)
C)
prime
D)
(a2b +10c)(ab –10c)
B
Subtract the polynomials. Assume all variable exponents represent whole numbers.
199)
(5y2n +3yn– 1) – (6y2n +8yn+3)
199)
A)
y2n – 5yn– 4
B)
–y2n + 5yn– 4
C)
–y2n – 5yn+ 2
D)
–y2n – 5yn– 4
D
Factor the trinomial by grouping, or state that the trinomial is prime.
200)
2x2+3xy +y2
200)
A)
(2x + y)(x + y)
B)
prime
C)
(2x – y)(x – y)
D)
(2x + y)(x +2y)
A
48
C
Factor any perfect square trinomial, or state that the polynomial is prime.
201)
x2– 20x + 400
201)
A)
(x + 20)(x – 20)
B)
(x – 20)2
C)
prime
D)
(x + 20)2
Solve the polynomial equation.
202)
42x2– 72x = 0
202)
A)
{0}
B)
0, 12
7
C)
12
7, 72
D)
12
7
Solve the problem.
203)
A projectile is fired straight upward. The function f(t) = – 16t2+56t describes the height of the
projectile, f(t), in feet, t seconds after firing. Factor the polynomial –16t2+56t and write the function
in factored form. Use the factored form of the function to find f(3).
203)
A)
f(t) = – 8t(2t –7); 120 ft
B)
f(t) = – 8t(2t –7); 24 ft
C)
f(t) = t(–16t +56); 120 ft
D)
f(t) = t(–16t +56); 24 ft
Factor out the negative of the greatest common factor. Assume any variable exponents represent whole numbers.
204)
–x2+5x –3
204)
A)
–1(x2+5x –3)
B)
–15(x2– x + 1)
C)
–x(x2–5x +3)
D)
–1(x2–5x +3)
Factor completely, or state that the polynomial is prime.
205)
3x3–75x
205)
A)
x(x +5)(3x –15)
B)
3x(x +5)(x –5)
C)
prime
D)
3(x +5)(x2–5x)
Solve the problem.
206)
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 a women’s average monthly weight loss if she exercised an average of 45
minutes per week.
206)
A)
1.1 lb
B)
2.6 lb
C)
2.1 lb
D)
1.5 lb
Factor completely, or state that the polynomial is prime.
207)
2x4–32
207)
A)
prime
B)
2(x +2)2(x –2)2
C)
2(x2+4)(x +2)(x –2)
D)
2(x2+4)(x2–4)
Factor the trinomial by grouping, or state that the trinomial is prime.
208)
2x2+13x +21
208)
A)
(2x +7)(x +3)
B)
(2x +7)(2x +3)
C)
(2x +3)(x +7)
D)
prime
50
Add the polynomials. Assume all variable exponents represent whole numbers.
209)
(4x2y –8xy +11) + (–3x2y +10xy –12)
209)
A)
–x2y – 18xy + 23
B)
2x3y2– 1
C)
x2y + 2xy – 1
D)
7x2y + 18xy + 23
Solve the problem.
210)
Find the lengths of the three sides of the right triangle in the figure shown.
16 2x –4
x
210)
A)
12 units, 16 units, 20 units
B)
8 units, 12 units, 16 units
C)
3 units, 4 units, 5 units
D)
12 units, 16 units, 28 units
A
Perform the indicated operations.
211)
(9x + 10y)(3x + 2y)
211)
A)
27x2+ 48xy + 48y2
B)
27x2+ 18xy + 20y2
C)
27x2+ 30xy + 20y2
D)
27x2+ 48xy + 20y2
D
Factor completely, or state that the trinomial is prime.
212)
48x3+140x2+100x
212)
A)
4x(25x +5)(x +5)
B)
prime
C)
4x(4x + 1)(3x +25)
D)
4x(4x +5)(3x +5)
D
51
C
Factor completely, or state that the polynomial is prime.
213)
x4+6x3+8x +48
213)
A)
(x +6)(x3+8)
B)
(x +6)(x –2)(x2+2x +4)
C)
prime
D)
(x +6)(x +2)(x2–2x +4)
Multiply the monomials. Assume any variable exponents represent whole numbers.
214)
(–9x3)(8x2)
214)
A)
–72x6
B)
72x5
C)
–72x5
D)
72x6
Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
215)
6xn12x3n– 5xn–1
10 x
215)
A)
72x4n – 30x2n –3
5xn + 1
B)
72x4n – 30x2n –3
5xn
C)
72x4n + 30x2n +3
5xn + 1
D)
72x4n – 30xn–3
5xn + 1
Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
216)
(4xy2– xy)2
216)
A)
16x2y2–8x2y3+x2y2
B)
16x2y4–8x2y3+x2y2
C)
16x2y4–4x2y3+x2y2
D)
4x2y4–8x2y3+x2y2
Write an expression in completely factored form for the area of the shaded figure.
217)
217)
A)
(x – y)(x – 3y)
B)
5(x – y)2
C)
(x – 5y)2
D)
(x – 2y)(x – 3y)
Factor out the negative of the greatest common factor. Assume any variable exponents represent whole numbers.
218)
–9x3–36x2+54x
218)
A)
–9x(x2+4x –6)
B)
–9(x3+4x2–6x)
C)
–x(9x2–36x +54)
D)
–9x(x2–4x +6)
Solve the problem.
219)
One end of a wire that is 10 meters long is attached to the top of a tower. The other end of the wire
is staked to the ground so that the wire is taut. The distance from the top of the tower to the bottom
of the tower is 2 meters greater than the distance from the bottom of the tower to where the wire is
staked down. How far is the stake from the base of the tower?
219)
A)
8 m
B)
6 m
C)
5 m
D)
9 m
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
220)
(1 +x3)(1 –x3)
220)
A)
2 –x9
B)
1 –x6
C)
2 –x6
D)
1 –x9
53
Factor completely, or state that the polynomial is prime.
221)
x3–3x2–4x +12
221)
A)
prime
B)
(x +3)(x +2)(x –2)
C)
(x –3)(x –2)2
D)
(x –3)(x +2)(x –2)
Give the degree and the leading coefficient of the polynomial.
222)
2xy4–11x3y9+12xy4
222)
A)
degree: 12; leading coefficient: 2
B)
degree: 12; leading coefficient: 11
C)
degree: 4; leading coefficient: 2
D)
degree: 12; leading coefficient: –11
Factor completely, or state that the polynomial is prime.
223)
9x5–9xy2
223)
A)
prime
B)
9x(x2– y)2
C)
9x(x2+ y)(x2– y)
D)
9x(x2+y2)(x + y)(x – y)
Solve the problem.
224)
Find the area of the rectangle by multiplying the length and the width of the large rectangle using
the FOIL method.
x 5
x
9
224)
A)
x2+45
B)
x2+14x
C)
x2+28x +45
D)
x2+14x +45
54
Factor completely, or state that the polynomial is prime.
225)
x4– 15x2+ 56
225)
A)
(x2+ 7)(x2– 8)
B)
(x2– 7)(x2+ 8)
C)
(x2– 7)(x2– 8)
D)
(x2+ 7)(x2+ 8)
Determine whether the graph shown is the graph of a polynomial function.
226)
226)
A)
Yes
B)
No
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
227)
(x – y +7)(x – y –7)
227)
A)
x2+y2–49
B)
x2–14y +y2–49
C)
x2– 2xy +y2–14x +14y –49
D)
x2– 2xy +y2–49
55
Add the polynomials. Assume all variable exponents represent whole numbers.
228)
1
8x4+2
5x3–1
6x + 7 + – 5
8x4–1
5x3+1
3x – 9
228)
A)
–1
2x4+1
5x3+1
6x – 2
B)
3
4x4+3
5x3+1
2x + 16
C)
3
4x8+3
5x6+1
2x2+ 16
D)
1
8x8+2
5x6–1
6x2+ 7
Evaluate the polynomial function.
229)
If f(x) =x2– 2x + 3, find f(a + h) – f(a).
229)
A)
2ah +h2– 2a
B)
2ah +h2– 2a + 6
C)
a2+ 2ah +h2– 2a – 2h + 3
D)
2ah +h2– 2a – 2h
Find the product. Assume all variable exponents represent whole numbers.
230)
(x –12)(x2+9x –7)
230)
A)
x3+21x2+115x +84
B)
x3– 3x2–115x +84
C)
x3+21x2+101x –84
D)
x3– 3x2– 101x –84
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
231)
(y3–9)(y3+9)
231)
A)
y6–18
B)
y9–81
C)
y6–81
D)
y9–18
56
Factor completely, or state that the trinomial is prime.
232)
5x3y3– 5x3y2– 30x3y
232)
A)
prime
B)
x3(5y2+ 10y)(y – 3)
C)
5x3y(y + 2)(y – 3)
D)
5x3y(y – 2)(y + 3)
Factor completely, or state that the polynomial is prime.
233)
36x2+ 25y2
233)
A)
(6x + 5y)2
B)
(6x + 5y)(6x – 5y)
C)
prime
D)
(6x – 5y)2
C
Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
234)
(2x – 9y)2
234)
A)
2x2+ 81y2
B)
4x2+ 81y2
C)
2x2– 36xy + 81y2
D)
4x2– 36xy + 81y2
D
235)
(5x + 7y)2
235)
A)
25x2+ 49y2
B)
5x2+ 49y2
C)
25x2+ 70xy + 49y2
D)
5x2+ 70xy + 49y2
C
57
C
Multiply the monomials. Assume any variable exponents represent whole numbers.
236)
(–10x5nyn +6)1
12 xny3
236)
A)
–5
6x6nyn +9
B)
–5
6x6ny2n +9
C)
–5
6x5nyn +9
D)
–5
6x5n2y3n +18
Use factoring to solve the quadratic equation.
237)
(x + 2)2+ 4(x – 3) = 7x + 12
237)
A)
–2, –12
7, 2, 3
B)
–2, –12
7, 3
C)
{–5, 4}
D)
{–4, 5}
238)
x2– 81 = 0
238)
A)
{10}
B)
{9, –9}
C)
{9}
D)
{–10, 10}
Subtract the polynomials. Assume all variable exponents represent whole numbers.
239)
(5x2n + 4xn– 7) – (2x2n – 10xn+ 18)
239)
A)
3x2n + 14xn+ 11
B)
3x4n + 14x2n – 25
C)
3x2n + 14xn– 25
D)
3x2n + 6xn+ 11
Use factoring to solve the quadratic equation.
240)
(x +9)(x + 1) =33
240)
A)
{–2, 12}
B)
{–9, –1}
C)
{–12, 2}
D)
{1, 9}
58
Factor any perfect square trinomial, or state that the polynomial is prime.
241)
x4+ 12x2+ 36
241)
A)
(x2+ 6)2
B)
(x2– 6)2
C)
prime
D)
(x + 6)2
Factor any difference of two squares, or state that the polynomial is prime. Assume any variable exponents represent
whole numbers.
242)
4– 81y2
242)
A)
prime
B)
(2 + 9y)2
C)
(2 – 9y)2
D)
(2 + 9y)(2– 9y)
Factor completely, or state that the trinomial is prime.
243)
4x3– 28x2+ 40x
243)
A)
prime
B)
(x – 2)(4x2– 20x)
C)
4x(x – 10)(x + 1)
D)
4x(x – 2)(x – 5)
Factor by grouping. Assume any variable exponents represent whole numbers.
244)
3x3+ 15x2+ 7x + 35
244)
A)
(x + 5)(3x2+ 7)
B)
(x + 5)(3x + 7)
C)
(x – 5)(3x2+ 7)
D)
(x + 5)(3x2– 7)
Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
245)
x5–11x2
245)
A)
x(x4–11x)
B)
x(x3–11)
C)
x2(x3–11)
D)
x2(x4–11)
Solve the problem.
246)
Find the formula for the area of the shaded region and express it in factored form.
3 y
3
y
246)
A)
(y +3)(y –3)
B)
(y –3)2
C)
(y +3)2
D)
y2+9
Evaluate the polynomial function.
247)
If f(x) =x2– 6x + 7, find f(a + h).
247)
A)
a2+ ah +h2– 6a – 6h – 6
B)
a2+h2– 6a – 6h + 14
C)
a2+h2– 6a – 6h + 7
D)
a2+ 2ah +h2– 6a – 6h + 7
Factor completely, or state that the trinomial is prime.
248)
8y4+80y3+192y2
248)
A)
y2(y +4)(8y +48)
B)
8(y2+4)(y2+6)
C)
8y2(y +4)(y +6)
D)
8y(y2+4y)(y +6)
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