Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
249)
(9an+ 13)(9an 13)
249)
A)
81an 169
B)
81a2n 169
C)
81a2n + 234an 169
D)
9a2n 169
Perform the indicated operations.
250)
Let f(x) =x2+ 8x + 5. Find f(a + h) f(a) and simplify.
250)
A)
2ah +h2+ 8a + 10
B)
2ah +h2+ 8h
C)
2ah +h2+ 8a + 8h
D)
a2+ 2ah +h2+ 8a + 8h + 5
B
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
251)
5a2+ 18ab 8b2
251)
A)
(5a 2b)(a +4b)
B)
prime
C)
(5a +2b)(a 4b)
D)
(5a +4b)(a 2b)
A
Factor completely, or state that the trinomial is prime.
252)
3y2+ 21y + 30
252)
A)
3(y + 5)(y + 2)
B)
3(y + 10)(y + 1)
C)
prime
D)
(y + 5)(3y + 6)
A
Factor the trinomial by grouping, or state that the trinomial is prime.
253)
5x2+46x 48
253)
A)
prime
B)
(5x 8)(x +6)
C)
(5x 6)(x +8)
D)
(5x +6)(x 8)
A
61
B
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
254)
2x2 11xy 21y2
254)
A)
(2x +3y)(x 7y)
B)
y(2x +3)(x 7)
C)
(2x +7y)(x 3y)
D)
prime
Factor any difference of two squares, or state that the polynomial is prime. Assume any variable exponents represent
whole numbers.
255)
a2(b +7)2
255)
A)
prime
B)
(a + b +7)(a b 7)
C)
(a + b +7)(a b +7)
D)
(a b +7)(a b 7)
B
Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
256)
(5x39)(x210)
256)
A)
5x559x3+90
B)
5x550x39x2+90
C)
5x550x39x290
D)
6x515x310x2+19
B
Factor by grouping. Assume any variable exponents represent whole numbers.
257)
x3+ 2x2 5x 10
257)
A)
(x 5)(x2+ 2)
B)
(x 2)(x2+ 5)
C)
(x + 2)(x 5)
D)
(x + 2)(x2 5)
D
Factor completely, or state that the polynomial is prime.
258)
9x2y2441y2
258)
A)
y2(x +7)(9x 63)
B)
9y2(x +7)(x27x)
C)
prime
D)
9y2(x +7)(x 7)
D
A
Add the polynomials. Assume all variable exponents represent whole numbers.
259)
(6x5 7x2 8x) + (5x5+ 3x2 3x)
259)
A)
11x 4x5 11x2
B)
3x5+ 9x2 10x
C)
11x5 4x2 11x
D)
4x8
Find the product. Assume all variable exponents represent whole numbers.
260)
(x +10)(x2+6x 7)
260)
A)
x3+16x2+53x 70
B)
x3+16x2+67x 70
C)
x4+10x3+6x2+53x 70
D)
x3+16x2+67x +70
A
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
261)
(3x + 4)(3x 4)
261)
A)
9x2 24x 16
B)
9x2+ 24x 16
C)
9x2 16
D)
x2 16
C
Factor using the formula for the sum or difference of two cubes.
262)
y3+ 216
262)
A)
(y + 6)(y2 6y + 36)
B)
(y 216)(y2 1)
C)
(y 6)(y2+ 6y + 36)
D)
(y + 6)(y2+ 36)
A
Factor completely, or state that the trinomial is prime.
263)
4x3y5+ 8x2y5 60xy5
263)
A)
y5(4x2+ 12x)(x 5)
B)
prime
C)
4xy5(x + 3)(x 5)
D)
4xy5(x 3)(x + 5)
D
C
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
264)
15x2+ 26x + 8
264)
A)
prime
B)
(3x + 4)(5x + 2)
C)
(3x 4)(5x 2)
D)
(15x + 4)(x + 2)
Given the polynomial functions, find the product function and the specified value.
265)
Let f(x) = x +7 and g(x) =x211x 2. Find (fg)(x) and (fg)(6).
265)
A)
(fg)(x) =x3+ 18x2+ 79x + 14; (fg)(6) =404
B)
(fg)(x) =x3 11x2 2x; (fg)(6) = 192
C)
(fg)(x) =x3 4x2 79x 14; (fg)(6) = 416
D)
(fg)(x) =7x3+ 77x2 14x; (fg)(6) = 1344
Factor completely, or state that the polynomial is prime.
266)
x3+3x24x 12
266)
A)
(x +3)(x 2)2
B)
(x +3)(x +2)(x 2)
C)
(x 3)(x +2)(x 2)
D)
prime
Factor by grouping. Assume any variable exponents represent whole numbers.
267)
ab 6c ac +6b
267)
A)
(b + c)(a +6)
B)
(b c)(a +6)
C)
(b c)(a 6)
D)
(b + c)(a 6)
Factor completely, or state that the polynomial is prime. Assume any variable exponents represent whole numbers.
268)
ab425a3b2
268)
A)
a(b2+5ab)(b25ab)
B)
ab2(b 5a)2
C)
prime
D)
ab2(b +5a)(b 5a)
64
Factor completely, or state that the polynomial is prime.
269)
x2(a 8) +y2(8 a)
269)
A)
(a 8)(x2+y2)
B)
(a 8)(x + y)(x y)
C)
prime
D)
(8 a)(x + y)(x y)
270)
x4+256
270)
A)
prime
B)
(x2+16)2
C)
(x216)2
D)
(x2+16)(x +4)(x 4)
A
Factor the polynomial using the greatest common binomial factor.
271)
(x + 8)(y 2) + (x + 8)(y + 1)
271)
A)
(x + 8)(y 3)
B)
(x + 8)(y2 1)
C)
(x + 8)(2y 1)
D)
(x + 8)(y + 3)
C
Factor by grouping. Assume any variable exponents represent whole numbers.
272)
ax2+ ay2+ az2+ bx2+ by2+ bz2 cx2 cy2 cz2
272)
A)
(x2+y2+z2)(a + b + c)
B)
(x2y2+z2)(a + b c)
C)
(x2+y2z2)(a + b c)
D)
(x2+y2+z2)(a + b c)
D
Factor completely, or state that the polynomial is prime.
273)
36x2y4+ 96x3y2 108x2y
273)
A)
x2y(36y3+ 96xy 108)
B)
12x2y(3y3+ 8xy 9)
C)
prime
D)
12x2y2(3y2+ 8x 9)
B
65
B
Factor the trinomial, or state that the trinomial is prime.
274)
a2 11a + 28
274)
A)
(a 7)(a 4)
B)
(a + 7)(a + 1)
C)
(a + 7)(a 4)
D)
prime
Factor any difference of two squares, or state that the polynomial is prime. Assume any variable exponents represent
whole numbers.
275)
(x 5)2y2
275)
A)
(x +5+ y)(x 5 y)
B)
prime
C)
(x +5 y)(x 5 y)
D)
(x 5+ y)(x 5 y)
Factor the polynomial using the greatest common binomial factor.
276)
14x2(10x 1) +10x 1
276)
A)
14x2(10x 1)
B)
(10x 1)(14x2+ 1)
C)
(10x 1)(14x2 1)
D)
(10x + 1)(14x2+ 1)
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
277)
[(7x 4) + 8y][(7x 4) 8y]
277)
A)
49x2 56x + 16 64y2
B)
49x2 56x + 16 + 112xy 64y + 64y2
C)
49x2 56x + 16 + 64y2
D)
49x2+ 56x + 16 64y2
Use factoring to solve the quadratic equation.
278)
x2 x =56
278)
A)
{1, 56}
B)
{7, 8}
C)
{7, 8}
D)
{7, 8}
Factor by grouping. Assume any variable exponents represent whole numbers.
279)
xy +2y +3x +6
279)
A)
(xy +2)(y +3)
B)
(x +3)(y +2)
C)
(x +2)(xy +3)
D)
(x +2)(y +3)
280)
x2ax +bx ab
280)
A)
(x +a)(xb)
B)
(x a)(x+b)
C)
(x +a)(x+b)
D)
(x a)(xb)
Give the requested components for the polynomial.
281)
7x89x5y5 xy2+6; the leading term and the coefficient of each term
281)
A)
leading term: 7x8; coefficients: 7, 9, 1, and 6
B)
leading term: 9x5y5; coefficients: 7, 9, 1, and 6
C)
leading term: 10; coefficients: 8, 10, 3, and 0
D)
leading term: 8; coefficients: 8, 5, and 1
Solve the problem.
282)
A herd of elk is introduced to a wildlife refuge. The number of elk, N(t), after t years is described by
the polynomial function N(t) = t3+17t +100. Use the Leading Coefficient Test to determine the
graph’s end behavior. What does this mean about what will eventually happen to the elk
population?
282)
A)
The elk population in the refuge will reach a constant amount greater than 0.
B)
The elk population in the refuge will grow out of control.
C)
The elk population in the refuge will be displaced by “oil” wells.
D)
The elk population in the refuge will die out.
Factor the trinomial by grouping, or state that the trinomial is prime.
283)
9a2 18ab + 8b2
283)
A)
(3a 2b)(3a 4b)
B)
prime
C)
(9a 2b)(a 4b)
D)
(3a + 2b)(3a + 4b)
Factor completely, or state that the polynomial is prime. Assume any variable exponents represent whole numbers.
284)
20 5y2
284)
A)
(10 + y)(10 y)
B)
prime
C)
5(2 + y)(2 y)
D)
(2 +5y)(25y)
C
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
285)
5x2+49x +36
285)
A)
(5x +9)(x +4)
B)
(5x +4)(5x +9)
C)
(5x +4)(x +9)
D)
prime
C
Solve the problem.
286)
Find the formula for the area of the shaded region and express it in factored form.
4 4
4 4
9y
4 4
4 4
9y
286)
A)
(9y +8)(9y 8)
B)
(9y +4)(9y 4)
C)
(9y 4)2
D)
(9y 8)2
A
A
Factor completely, or state that the polynomial is prime.
287)
2x3+2
287)
A)
prime
B)
2(x + 1)(x2 x + 1)
C)
2(x + 1)(x2+ x + 1)
D)
2(x 1)(x2+ x + 1)
Factor by grouping to obtain the difference of two squares.
288)
x2 10x + 25 x4
288)
A)
(x + 5 +x2)(x + 5 x2)
B)
(x 5 +x2)(x 5 x2)
C)
(x 5 +x2)(x + 5 x2)
D)
(x + 5 +x2)(x 5 x2)
Solve the problem.
289)
The function V(x) =3x3+17x2+20x describes the volume of the box shown, in cubic inches, whose
height is x inches. Factor the expression for V(x) and write the function in completely factored form.
Use the factored form of the function to find V(2).
xx +4
3x +5
289)
A)
V(x) = x(3x +4)(x +5); 140 in.3
B)
V(x) = (3x2+4x)(x +5); 140 in.3
C)
V(x) = x(3x +5)(x +4); 132 in.3
D)
V(x) = (3x2+5x)(x +4); 132 in.3
69
290)
An object is thrown upward from the top of a 160foot building with an initial velocity of 48 feet
per second. The height h of the object after t seconds is given by the quadratic equation
h = 16t2+ 48t + 160. When will the object hit the ground?
290)
A)
3 sec
B)
5 sec
C)
160 sec
D)
2 sec
Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
291)
[(7x 2) + 8y]2
291)
A)
49x2 14x + 4 + 56xy + 16y + 64y2
B)
49x2 28x + 4 + 112xy 32y + 64y2
C)
49x2 28x + 112xy 32y + 64y2
D)
49x2 28x + 4 + 56xy + 16y + 64y2
Factor completely, or state that the trinomial is prime.
292)
2y3 4y2 16y
292)
A)
(2y2+ 4y)(y 4)
B)
2y(y 2)(y + 4)
C)
(y 2)(2y2+ 8)
D)
2y(y + 2)(y 4)
Factor completely, or state that the polynomial is prime. Assume any variable exponents represent whole numbers.
293)
x4n 81
293)
A)
(xn+3)2(xn3)2
B)
(x2n +9)(xn+3)(xn3)
C)
prime
D)
(x2n +9)(x2n 9)
Factor completely, or state that the polynomial is prime.
294)
162x4y 2y5
294)
A)
2y(81x2+y2)(9x + y)(9x y)
B)
prime
C)
2(9x2+y2)(3x + y)(3x y)
D)
2y(9x2+y2)(3x + y)(3x y)
Determine whether the graph shown is the graph of a polynomial function.
295)
295)
A)
Yes
B)
No
Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers.
296)
(7x + y)2
296)
A)
49x2+7xy +y2
B)
49x2+14xy +y2
C)
49x2+14xy + 2y2
D)
7x2+14xy +y2
Factor completely, or state that the polynomial is prime.
297)
128x5 54x2
297)
A)
2x2(4x 3)(16x2 12x + 9)
B)
prime
C)
2x2(4x 3)(16x2+ 12x + 9)
D)
2x2(4x + 3)(16x2 12x + 9)
Solve the problem.
298)
A rectangular park measuring 20 yards by 22 yards is surrounded by a trail of uniform width. If the
area of the park and the trail combined is 1088 square yards, what is the width of the path?
298)
A)
5 yd
B)
8 yd
C)
6 yd
D)
7 yd
Use factoring to solve the quadratic equation.
299)
2x2 16x + 30 = 0
299)
A)
{3, 5}
B)
{3, 5}
C)
{2, 3, 5}
D)
{0, 3, 5}
Factor completely, or state that the polynomial is prime.
300)
2x37x2
300)
A)
prime
B)
x(2x27x)
C)
x2(2x 7)
D)
x2(2 7x)
Solve the problem.
301)
The area of the floor plan with semicircular ends shown is A = 4rw +r2. Express the area, A, in
factored form.
301)
A)
A = rw(4 +r)
B)
A =r(4w +r)
C)
A = r(4w +r)
D)
A =r2(4w +)
72
Factor any difference of two squares, or state that the polynomial is prime. Assume any variable exponents represent
whole numbers.
302)
x2n 36
302)
A)
(x2n +6)(x2n 6)
B)
(x +6)(x 6)
C)
(xn+6)(xn6)
D)
prime
Solve the problem.
303)
If the cost, C(x), for manufacturing x units of a certain product is given by C(x) =x2 60x + 9100,
find the number of units manufactured at a cost of $11,800.
303)
A)
30 units
B)
70 units
C)
130 units
D)
90 units
304)
A machine produces open boxes using square sheets of plastic. The machine cuts equalsized
squares measuring 4 inches on a side from each corner of the sheet, and then shapes the plastic into
an open box by turning up the sides. If each box must have a volume of 1600 cubic inches, find the
length of one side of the open box.
304)
A)
28 in.
B)
24 in.
C)
19 in.
D)
20 in.
Subtract the polynomials. Assume all variable exponents represent whole numbers.
305)
(2x5 13x2 12) (4x5+ 10x2+ 10)
305)
A)
2x5 9x2 2
B)
2x5 23x2 22
C)
47x7
D)
2x5 23x2 2
Factor completely, or state that the trinomial is prime.
306)
4x2 28x + 40
306)
A)
4(x 10)(x + 1)
B)
(x 5)(4x 8)
C)
prime
D)
4(x 5)(x 2)
Give the requested components for the polynomial.
307)
x52x4y8+11xy 7x +12; degree of each term and degree of the polynomial
307)
A)
degrees: 1, 2, 11, 7, 12; degree of polynomial: 2
B)
degrees: 5, 12, 2, 1, 0; degree of polynomial: 12
C)
degrees: 5, 4, 1, 1, 0; degree of polynomial: 5
D)
degrees: 5, 4, 2, 0; degree of polynomial: 19
Solve the problem.
308)
Each side of a square is lengthened by 2 inches. The area of this new, larger square is 49 square
inches. Find the length of a side of the original square.
308)
A)
5 in.
B)
9 in.
C)
2 in.
D)
7 in.
A
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
309)
6x2 5xy 6y2
309)
A)
prime
B)
(6x 3y)(x + 2y)
C)
(2x 3y)(3x + 2y)
D)
(2x + 3y)(3x 2y)
C
Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent
whole numbers.
310)
(x 5)(x +5)(x2+25)
310)
A)
x4+10x3250x 625
B)
x4+10x3+50x2250x 625
C)
x4+50x2+625
D)
x4625
D
74
B
Factor by grouping to obtain the difference of two squares.
311)
z2x2+ 6xy 9y2
311)
A)
(z + x 3y)(z x + 3y)
B)
(z + x + 3y)(z x 3y)
C)
(z + x + 3y)(z x + 3y)
D)
(z + x 3y)(z x 3y)
Factor by grouping. Assume any variable exponents represent whole numbers.
312)
ay2+ 3by2 3ax 9bx
312)
A)
(a + 3b)(y2+ 3x)
B)
(a 3b)(y2+ 3x)
C)
(a + 3b)(y2 3x)
D)
(a 3b)(y2 3x)
Factor completely, or state that the polynomial is prime. Assume any variable exponents represent whole numbers.
313)
x2+36y2
313)
A)
(x 6y)2
B)
(x +6y)(x 6y)
C)
(x +6y)2
D)
prime
314)
6x56xy4
314)
A)
6x(x + y)2(x y)2
B)
6x(x2+y2)(x2y2)
C)
prime
D)
6x(x2+y2)(x + y)(x y)
Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
315)
11xy(5x 9y)
315)
A)
16x2y 20xy2
B)
16x220y2
C)
55x2y 99xy2
D)
55x299y2
Find the product. Assume all variable exponents represent whole numbers.
316)
(x2+ x + 6)(x2+ x + 2)
316)
A)
x4+x3+ 8x2+ 8x +12
B)
x4+ 2x3 8x2+ 4x +12
C)
x4+x3 7x2 8x +12
D)
x4+ 2x3+ 9x2+ 8x +12
Use the method of your choice to factor the trinomial, or state that the trinomial is prime.
317)
9a2 18ab + 8b2
317)
A)
(3a 4b)(3a 2b)
B)
prime
C)
(3a + 4b)(3a + 2b)
D)
(9a 4b)(a 2b)
A
Solve the problem.
318)
After 4 years, the balance, A, in an account with principal P and interest rate r compounded
annually is given by the formula A = P(1 + r)3+ P(1 + r)3r. Use factoring by grouping to simplify
this formula.
318)
A)
A = P(1 + Pr)(1 + r)3
B)
A = (P + Pr)(1 + r)3
C)
A = P(1 + r)4r
D)
A = P(1 + r)4
D
Factor completely, or state that the trinomial is prime.
319)
4x3+ 4x2 24x
319)
A)
4x(x 2)(x + 3)
B)
4x(x + 2)(x 3)
C)
(x 2)(4x2+ 12)
D)
(4x2+ 8x)(x 3)
A
Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
320)
(x 11y)(x + 5y)
320)
A)
x2 6xy 55y2
B)
x2 6xy 6y2
C)
x 6xy 55y
D)
x2 9xy 55y2
A
76
D
Solve the problem.
321)
A baseball is thrown straight up from the rooftop 160 feet high. The function s(t) = 16t2+48t +160
describes the ball’s height above the ground, s(t), in feet, t seconds after it was thrown. How long
will it take for the ball to hit the ground?
321)
A)
80 sec
B)
2 sec
C)
6 sec
D)
5 sec
Factor completely, or state that the polynomial is prime.
322)
x3xy2+x2yy3
322)
A)
prime
B)
(x +y)2(x y)
C)
(x +y)(xy)
D)
(x y)2(x +y)
Given the polynomial functions, find the product function and the specified value.
323)
Let f(x) = x +12 and g(x) = x 1. Find (fg)(x) and (fg)(2).
323)
A)
(fg)(x) =x2+ 11x 12; (fg)(2) = 30
B)
(fg)(x) =x2 11x 12; (fg)(2) =14
C)
(fg)(x) =x2+ 11x +12; (fg)(2) = 6
D)
(fg)(x) =x2+ 13x +12; (fg)(2) = 10
Write an expression in completely factored form for the area of the shaded figure.
324)
10y
10y
x
x10y
x
10y
324)
A)
x2+10xy +100y2
B)
10(x + y)2
C)
x2+20xy +100y2
D)
(x +10y)2
Factor by introducing an appropriate substitution.
325)
(x +6)29(x +6) +20
325)
A)
(x2+6x 5)(x2+6x 4)
B)
(x + 11)(x + 10)
C)
(x + 1)(x + 2)
D)
(x26x +5)(x26x +4)
Factor the polynomial using the greatest common binomial factor.
326)
a(x +14) +8(x +14)
326)
A)
8a(x +14)
B)
14x(a +8)
C)
(ax +14a) + (8x +112)
D)
(x +14)(a +8)
D
Solve the problem.
327)
The following table shows the number of DWI arrests in a certain state for the past five years.
Year DWI arrests
1 4147
24197
34247
44280
54329
The polynomial function f(x) = 0.65x3+0.51x2+60.44x +4087 models the number of DWI arrests
over the past five years. Use this function to predict the number of DWI arrests in year 15. Round to
the nearest whole number.
327)
A)
1164 DWI arrests
B)
2008 DWI arrests
C)
2915 DWI arrests
D)
2907 DWI arrests
C
Factor completely, or state that the polynomial is prime.
328)
x4+ 9x2400
328)
A)
(x +4)(x 4)(x2+25)
B)
(x216)(x2+25)
C)
(x +4)(x 4)(x +5)(x 5)
D)
(x 4)2(x2+25)
A
78
C
Use factoring to solve the quadratic equation.
329)
x2+16x = 64
329)
A)
{8}
B)
{8, 8]
C)
{2 2}
D)
{8}
Factor completely, or state that the polynomial is prime. Assume any variable exponents represent whole numbers.
330)
1 16y4
330)
A)
(1 +2y)2(1 2y)2
B)
(1 +4y2)(1 +2y)(1 2y)
C)
prime
D)
(1 +4y2)(1 4y2)
Subtract the polynomials. Assume all variable exponents represent whole numbers.
331)
(4x6 4x4 7x) (7x6+ 17x4+ 19x)
331)
A)
3x6 21x4+ 12x
B)
50x11
C)
3x6 21x4 26x
D)
3x6+ 3x4+ 12x
Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
332)
y2+12y
332)
A)
12(y2+ y)
B)
y2(1 +12y)
C)
12y(y + 1)
D)
y(y +12)
Factor using the formula for the sum or difference of two cubes.
333)
y9+ 512
333)
A)
(y3+ 8)(y6 8y3+ 64)
B)
(y2+ 8)(y4 8y2+ 64)
C)
(y + 8)(y2 8y + 64)
D)
(y + 2)(y2 2y + 4)(y6 8y3+ 64)
79
Factor any difference of two squares, or state that the polynomial is prime. Assume any variable exponents represent
whole numbers.
334)
169x2 36y2
334)
A)
prime
B)
(13x 6y)2
C)
(13x + 6y)2
D)
(13x + 6y)(13x 6y)
Factor the trinomial, or state that the trinomial is prime.
335)
y2+ 9y + 8
335)
A)
(y + 1)(y + 8)
B)
prime
C)
(y 1)(y + 1)
D)
(y 1)(y + 8)
A
Solve the polynomial equation.
336)
4x2=610x
336)
A)
2, 3
B)
0, 5
2
C)
1
2,3
D)
0, 5
2
C
Factor by introducing an appropriate substitution.
337)
5x4+37x2+14
337)
A)
(5x2+2)(x2+7)
B)
x(5x2+2)(x +7)
C)
x2(5x +2)(x +7)
D)
(5x2+ x +2)(x2+ x +7)
A
Factor the trinomial by grouping, or state that the trinomial is prime.
338)
10x2+ 9x 9
338)
A)
(2x + 3)(5x 3)
B)
prime
C)
(2x 3)(5x + 3)
D)
(10x + 3)(x 3)
A
80
D