Download gcf (lef+overs) ...then check the (lef+overs) for other factoring! D O

gcf (lef+overs)
...then check the (lef+overs) for other factoring!
Difference (Subtraction?) Case II Trinomial
Leading coefficient?
Of
(don't forget to check for a GCF)
Two (Binomial?)
Find your factors & signs
Squares (both perfect?)
Rewrite as 4 terms
a2 - b2 = (a + b)(a - b)
Factor by grouping (GCF each)
Rearrange
Case I Trinomial
No leading coefficient?
Factor by grouping
Find your factors & signs
Put terms in descending order,
Drop & done!
or with other like-factor terms
Group terms in sets of 2
Factor each group
Rearrange
QUESTION #9 (in the case I trinomial section) and QUESTION #11 (in the factor
by grouping section) changed. SEE UPDATED REVIEW SHEET ON MY WEBSITE!
Chapter 1: Polynomials
REVIEW SHEET ANSWER KEY
Factor each of the following using the GCF:
1) z(12x – 7y)
2) 2x(2x – 3)
3) 3x3(5 – 3x)
4) 27x2y2(x2 – 2y2)
5) 8xz(10y + 9xz2)
6) 4xy(-12x + 5y2)
7) 8x2(3x2 – 2)
8) 15x2y2z(-x2 + 2z)
9) 4xy(2x – 3x2y2 + 4y)
10) 3xy2(8x2 + 5y – 11x)
11) 5(3x3 + 5 – 8x2)
12) 9xy2(2x3 – 4xy3 + 3y2)
Factor each of the following (DOTS or Perfect Squares)
1) (p – 9)(p + 9)
2) (x – 6)(x + 6)
3) (b – 11)(b + 11)
4) 4(s – 6)(s + 6)
5) 5(g – 7)(g + 7)
6) 25(k – 3)(k + 3)
7) (2x – 3y)(2x + 3y)
8) (4x – 9)(4x + 9)
9) (3 – x)(3 + x)
Factor each of the following (Case 1 trinomials)
1) (w – 12)(w + 11)
2) (x – 3)(x + 16)
3) (z + 12)(z – 3)
4) (h + 6)(h + 6)
5) (r + 9)(r - 4)
6) (b – 9)(b + 4)
7) (m – 18)(m – 2)
8) (y – 10)(y + 6)
9) (v - 10)(v - 6)
10) (r – 5)(r + 12)
11) (x + 60)(x + 1)
12) (g – 20)(g – 3)
Factor each of the following: (by grouping- 4 terms)
1) (r – 8)(8r2 + 1)
2) (4p – 7)(3p2 + 7)
3) (2x2 – 5)(6x + 1)
4) (3v – 8)(2v2 + 7)
5) 3(7n + 6)(3n2 – 5)
6) 3(k – 4)(7k2 + 5)
7) (5v + 1)(5v2 + 6)
8) 5(3n + 5)(7n2 – 5)
9) (b – 3)(4b2 – 5)
10) (4n – m)(4m – 7)
11) (6m - n2)(7c + 6d)
12) (4y – 1)(x – 6)
Factor each of the following: (Case II)
1) (x – 6)(2x + 5)
2) (3s + 4)(4s + 1)
3) (3c + 2)(6c – 1)
4) (2y + 1)(9y + 5)
5) (3f – 1)(5f – 3)
6) (k + 1)(15k – 8)
7) 2(2s – 5)(3s + 2)
8) 6(d + 1)(4d – 5)
9) 3(w + 4)(7w + 3)
10) 5(x + 5)(8x + 1)
11) 10(2z + 1)(5z – 2)
12) 3(2r – 7)(4r – 1)
1) 7(f + 6)(f + 6)
2) 2(x – 10)(x + 9)
3) 9(k – 7)(k – 4)
4) 3x(1 – 2x)(1 + 2x)
5) 7(x + 1)(x + 3)
6) (4x2+9)(2x–3)(2x + 3)
7) 12(3x2 – 1)(3x2 + 1)
8) 3(x + 3)(2x + 1)
9) 4x(3 + 2y)
10) (3x – 2)(3x + 2)
11) 12(2x – y4)(2x + y4)
12) 8x(x – 3)(x – 3)
Factor Completely
Perform the indicated operation. (Addition/Subtraction/Multiplication/Division)
1) 5x + 10x2 – 2
2) -3y2 – 18y + 16
3) 41r + 8y + 6
4) 8y2 – 10y
5) b2 – 6b + 12
6) -22r + 23
7) 32c2 – 7c
8) -8y2 – 4y + 6
9) -9y2 - 6y
10) j3 – 2j2 – 4j + 33
7) k3 – 8k + 3
13) 72y2 – 42y – 15
14) 8u2 – 6u - 2
15) 3g4 – 14g3 + 8g2 + g – 4
16) -32m3 + 68m2 – 29m + 14
18) 5y8 – 3y17 + 2y
19) -3 – 4hk + 5h2
20) 2a – 1 + 3a6
21) 21pe – 14p2 + 1
12) 2p3 – 20p2 + 48p
17) 18y + 9 – 2y3 – y2