Download Review for MA098 Factoring

Review for MA098
Factoring
If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
1) 15x2 + 26x + 8
1)
Solve the problem.
2) The area of a circle is 100 square meters. Find its radius.
Factor.
3) 64x2 + 48xy + 9y2
3)
4) x2 + 10xy + 25y2
4)
Factor out the largest possible common factor.
5) 21y3 - 6y2 + 15y
Solve.
5)
6) x2 + 5x - 14 = 0
6)
Solve the equation.
7) 5x2 - 40x + 75 = 0
Factor.
2)
7)
8) 100 - x2 y2
8)
Solve the equation.
9) x2 + 4x - 60 = 0
9)
Factor by grouping.
10) 12x2 + 7xt - 12t2
10)
If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
11) 16x2 - 81
11)
Solve the equation.
12) 13d2 - 7d = 0
Solve the problem.
13) The equation D =
12)
1
n(n-3) gives the number of diagonals, D, for a polygon with n sides.
2
Find the number of sides n for a polygon that has 27 diagonals.
1
13)
Factor as completely as possible. If unfactorable, indicate that the polynomial is prime.
14) x2 - x - 35
14)
If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
15) 72a 4 - 98b2
15)
Factor by grouping.
16) 15x2 + 19x + 6
16)
Factor.
17) z 2 - 2z + 1
17)
Find a polynomial in factored form for the shaded region.
18)
18)
13
15
Factor out the largest possible common factor.
19) 6m 9 - 9m 7 - 18m 5
19)
Factor using the trial and error method.
20) 20x2 + 7x - 6
20)
Factor.
21) 49x2 - 9
21)
22) 64x2 + 144xy + 81y2
22)
Factor out the largest possible common factor.
23) 32x7 y9 - 24x2 y6 + 36x4 y4
23)
Factor as completely as possible. If unfactorable, indicate that the polynomial is prime.
24) x4 - 3x2 - 4
24)
Solve the equation.
x2 + 13x
= -11
25)
2
25)
2
Factor.
26) 6x2 - 6x - 36
26)
If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
27) 24xy - 20by + 18x - 15b
27)
Factor.
28) 81x2 + 144xy + 64y2
28)
If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
29) 36x + 12x2 - 12xy
29)
Factor by grouping.
30) 10z 2 + 11z - 6
30)
Solve the problem.
31) The width of a rectangle is 6 kilometers less than twice its length. If its area is 80 square
kilometers, find the dimensions of the rectangle.
31)
Factor.
32) s18 - t16
32)
Factor by grouping.
33) 9x - 108 + xy - 12y
33)
Solve the problem.
34) The force in newtons needed to stretch a certain spring x centimeters from its resting
position is given by the polynomial function f(x) = 8x2 where 8 is the spring constant. Find
the force needed to stretch the spring 3 centimeters.
35) The sum of two numbers is 10, and the sum of their squares is 52. Find the numbers.
34)
35)
If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
36) 4k3 m + 28k2 m 2 + 49km3
36)
Factor by grouping.
37) 12x2 + 10x - 18x - 15
37)
Factor.
38) x2 - x - 30
38)
Factor as completely as possible. If unfactorable, indicate that the polynomial is prime.
39) x3 + 3x2 - 25x - 75
3
39)
If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
40) 8x2 - 28x - 16
40)
Factor using the trial and error method.
41) 10x2 + 19x + 6
41)
Factor by grouping.
42) xy + 7x - 4y - 28
42)
If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
43) x4 - 256
43)
Factor out the largest possible common factor.
44) w(z - 12) - 8(z - 12)
44)
Solve the equation.
45) x2 + 9x - 64 = 3(x - 8)
45)
Factor.
46) x7 - 10x6 + 9x5
46)
Factor as completely as possible. If unfactorable, indicate that the polynomial is prime.
47) x4 + 2x3 + 125x + 250
47)
Factor.
48) x2 + 15x + 54
48)
Factor by grouping.
49) 7x2 - 5x - 2
49)
If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
50) 21x2 - 91x - 70
50)
4
Answer Key
Testname: FACTORING
1) (3x + 4)(5x + 2)
2) 10 m
3) (8x + 3y)2
4) (x + 5y)2
5) 3y(7y2 - 2y + 5)
6) x = -7, x = 2
7) x = 3, 5
8) (10 - xy)(10 + xy)
9) x = -10, 6
10) (3x + 4t)(4x - 3t)
11) (4x + 9)(4x - 9)
7
,0
12) d =
13
13) 9 sides
14) Prime
15) 2(6a 2 + 7b)(6a 2 - 7b)
16) (3x + 2)(5x + 3)
17) (z - 1)2
18) (13 - x)(15 + x)
19) 3m 5 (2m 4 - 3m 2 - 6)
20) (4x + 3)(5x - 2)
21) (7x + 3)(7x - 3)
22) (8x + 9y)2
23) 4x2 y4 (8x5 y5 - 6y2 + 9x2 )
24) (x + 2)(x - 2)(x2 + 1)
25) x = -11, -2
26) 6(x + 2)(x - 3)
27) (4y + 3)(6x - 5b)
28) (9x + 8y)2
29) 12x(3 + x - y)
30) (2z + 3)(5z - 2)
31) length = 8 km, width = 10 km
32) (s9 + t8 )(s9 - t8 )
33) (x - 12)(9 + y)
34) 72 newtons
35) 4 and 6
36) km(2k + 7m)2
37) (2x - 3)(6x + 5)
38) (x + 5)(x - 6)
39) (x + 5)(x - 5)(x + 3)
40) 4(2x + 1)(x - 4)
41) (2x + 3)(5x + 2)
42) (y + 7)(x - 4)
43) (x2 + 16)(x + 4)(x - 4)
44) (z - 12)(w - 8)
45) x = -10, 4
46) x5 (x - 9)(x - 1)
5
Answer Key
Testname: FACTORING
47) (x + 2)(x + 5)(x2 - 5x + 25)
48) (x + 6)(x + 9)
49) (7x + 2)(x - 1)
50) 7(3x + 2)(x - 5)
6