Chapter 5 Exam Review
Note: These are only a sample of the types of problems that may appear on the exam. Keep in mind, anything covered
in class may appear on the exam.
Give the requested components for the polynomial.
1) 5x8 y + x7y3 + 13y2 ; leading term and leading
Multiply using one of the rules for the square of a
binomial. Assume any variable exponents represent whole
numbers.
10) (5x + y)2
coefficient of the polynomial
Answer: leading term: x7 y3 ; leading coefficient: 1
Answer: 25x2 + 10xy + y2
Add the polynomials. Assume all variable exponents
represent whole numbers.
2) (-9x7 + 18x6 - 13) + (3x7 + 16x6 - 9)
11) (3x - 7y)2
Answer: 9x2 - 42xy + 49y2
Answer: -6x7 + 34x6 - 22
Multiply using the rule for the product of the sum and
difference of two terms. Assume any variable exponents
represent whole numbers.
12) (2x + 11y)(2x - 11y)
1
2
1
5
1
1
3) x4 + x3 - x + 7 + - x4 - x3 + x - 9
8
5
6
8
5
3
Answer: -
1 4 1 3 1
x + x + x-2
2
5
6
Answer: 4x2 - 121y2
13) (6x + 11)(6x - 11)
Subtract the polynomials. Assume all variable exponents
represent whole numbers.
4) (4x5 + 5x4 - 6x3 - 9) - (6x5 + 9x4 + 9x3 - 6)
Answer: 36x2 - 121
Use the Leading Coefficient Test to determine the end
behavior of the polynomial function. Then use this end
behavior to match the function with its graph.
14) f(x) = 6x3 - 3x2 - 3x - 2
Answer: -2x5 - 4x4 - 15x3 - 3
5) (5x4 y2 + 7x3 y + 6y) - (3x4 y2 + 10x3 y + 11y +
9x)
A) falls to the left and falls to the right
Answer: 2x4 y2 - 3x3 y - 5y - 9x
Multiply the monomials. Assume any variable exponents
represent whole numbers.
6) (3x4 y)(-6x 7 y2 )
Answer: -18x11y3
Multiply the monomial and the polynomial. Assume any
variable exponents represent whole numbers.
7) 12ab2 (9a 2 b3 + 10ab)
Answer: 108a3 b5 + 120a 2 b3
Find the product. Assume all variable exponents represent
whole numbers.
8) (p - q)(p2 + pq + q2 )
Answer: p3 - q3
9) (2x2 + 5x - 4)(x2 + 4x - 4)
Answer: 2x4 + 13x3 + 8x2 - 36x + 16
1
B) rises to the left and rises to the right
18) 3x2 (5x + 2) - 2(5x + 2)
Answer: (5x + 2)(3x2 - 2)
Factor by grouping, if possible.
19) x3 - 2x2 + 3x - 6
Answer: (x - 2)(x2 + 3)
20) 5x3 - 25x2 + 3x - 15
Answer: (x - 5)(5x2 + 3)
Factor completely. If the polynomial is prime, state this.
21) y2 + 7y - 30
C) rises to the left and falls to the right
Answer: (y + 10)(y - 3)
22) x2 + 27x + 28
Answer: Prime
23) - 4b - 96 + b2
Answer: (b + 8)(b - 12)
24) 3x2 - 21x + 30
Answer: 3(x - 5)(x - 2)
D) falls to the left and rises to the right
25) x2 +
2
1
x+
3
9
Answer: x +
1 2
3
26) 8x2 + 43x + 15
Answer: (8x + 3)(x + 5)
27) 9t2 - 18t + 8
Answer: (3t - 2)(3t - 4)
Answer: D
28) 8z 2 - 6z - 9
Answer: (2z - 3)(4z + 3)
Factor out the largest common factor.
15) a 5 - 37am 5 + 2a 3 m 6 - 17a 5 m 5
29) 18x2 - 63x - 36
Answer: a(a 4 - 37m 5 + 2a 2 m 6 - 17a 4 m 5 )
Answer: 9(2x + 1)(x - 4)
16) 108m 9 - 48m 4 - 24m 2
30) 6x2 + 17xt + 12t2
Answer: 12m 2 (9m 7 - 4m 2 - 2)
Answer: (3x + 4t)(2x + 3t)
Factor completely.
17) y(y + 10) - 8(y + 10)
Answer: (y + 10)(y - 8)
2
Determine whether the following is a perfect-square
trinomial.
31) x2 + 24x + 144
44) 2x +
6
5
4x -
Answer: -
Answer: Yes
32) x2 - 25x + 625
4
=0
7
3 1
,
5 7
Solve by factoring and using the principle of zero
products.
45) b2 + 18b = 0
Answer: No
33) x2 - 4x + 16
Answer: -18, 0
Answer: No
46) a 2 - 9a + 14 = 0
Factor completely. If the polynomial is prime, state this.
34) 36x2 - 84x + 49
Answer: 2, 7
47) 8x2 = 5x
Answer: (6x - 7)2
Answer:
35) x2 + 24x + 144
Answer: (x + 12)2
5
,0
8
48) 2x2 + 4 = x 2 + 5x
Determine whether the following is a difference of
squares.
36) x2 - 64y2
Answer: 4, 1
49) 3x(3x - 4) = -4
Answer: Yes
Answer:
37) x2 + 144
Solve.
Answer: No
Factor completely. If the polynomial is prime, state this.
38) 9x2 - 25
2
3
50) Use the given graph of y = x 2 - 3x - 4 to solve
x2 - 3x - 4 = 0.
Answer: (3x + 5)(3x - 5)
39) 64y4 - 81
Answer: (8y2 + 9)(8y2 - 9)
Factor completely.
40) 216p3 - 1
Answer: (6p - 1)(36p2 + 6p + 1)
41) 512s3 + 1
Answer: (8s + 1)(64s2 - 8s + 1)
Answer: -1, 4
42) t3 + 343
Solve the problem.
51) The product of two consecutive odd integers is
99. Find all pairs of integers that satisfy this
condition.
Answer: (t + 7)(t2 - 7t + 49)
Solve using the principle of zero products.
43) (x - 6)(x + 8) = 0
Answer: -11 and -9, 9 and 11
Answer: 6, -8
3
52) A lot is in the shape of a right triangle. The
shorter leg measures 120 meters. The
hypotenuse is 40 meters longer than the length
of the longer leg. How long is the longer leg?
Answer: 160 meters
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