Download Basic Algebra Final Review

BASIC ALGEBRA FINAL EXAM REVIEW
UNIT 8 FACTORING (BLUE NOTES)
Required Skills:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
Write the prime factorization of a number.
Identify the factors of a number.
Determine the greatest common factor of two monomials.
Factor a polynomial using the greatest common factor.
Factor a trinomial with a leading coefficient of 1.
Factor a trinomial with a leading coefficient other than 1.
Factor the difference of perfect squares.
Identify the sum of perfect squares as prime.
Factor trinomials by grouping.
Factor polynomials completely.
Solve polynomial equations by factoring.
Write each of the following numbers as a product of primes.
1)
40
2)
56
3)
250
4)
345
7)
100
8)
225
Identify all the factors of each number.
5)
28
6)
80
1
Find the missing factors.
9)
a11  ______  a23
10) a 7b3c4  ___________  a11b4c18d9
11)
4y3  __________  48y 7
12) 11x5 y2  __________  22x8 y2
13)
__________ 6mp8  42m6p13
14) 8d6wz7  ___________  48d6w5z16
State the greatest common monomial factor.
15) 16 and 44
16) 24 and 36
17) 25x9 and 90x12
18) 20y 7 w 9 and 28y5w
Factor the polynomial using the greatest common factor.
19) 3x2  27x  9
20) b4  3b3  7b2
21) 4y3  40y2  24y
22) 14a 5w6  49a 4w53  28a 2w 7
2
Factor each polynomial (if possible).
23) x2  5x  6
24) x2  25
25) y2  y  12
26) a 2  7a  18
27) w2  36
28) n2  16n  28
29) 2x2  23x  45
30) 4x2  4x  3
31) 5x2  17x  6
32) 3x2  13x  12
3
33) 4y2  4y  35
35)
4x3 – 10x2 + 14x - 35
34) 6u2  13u  15
36)
18ax – 15bx – 66a + 55b
Factor completely. Factor using the greatest common factor and then factor the
trinomial.
37)
2x2  16x  30
38)
2x3  32x
39)
5x2  10x  5
40)
4x3 y  2x2 y  2xy
4
Solve each of the following equations.
41)
x2 – 13x + 40 = 0
42)
x2 + 5x = 14
43)
3x2 + 7x + 4 = 0
44)
4x3 – 100x = 0
5