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Factoring Checklist Practice
Step 1: check for a GCF…always do this first.
 After factoring out a gcf (if there is one) proceed to step 2
Step 2: How many terms are there in expression (after factoring out the GCF)
2 terms
3 terms
Check to see if it’s the difference of perfect squares
Check to see if it’s a perfect square trinomial
X2 – 9
–4x2 + 100
36x2 – 25y2
x2 + 10x + 25
9x2 – 24x + 16
81x2 – 18x + 1
A perfect square minus a perfect square
1st and third terms are perfect squares, middle term is twice
The product of the square roots
YES: factor as 2 quantities:
YES: factor as 2 identical quantities,
(square root + square root)( square root – square root)
(square root + square root) choose sign of middle term
NO: Finished
NO: Multiply 1st term and third terms. Find factors of
The product that either + or – to get the middle term,
If you ever have x2 + 9, the expression is prime
sign of the third term tells you whether you should + or –
Re-write Polynomial so that it has four terms and group.
If this doesn’t work, the expression is prime
Watch for Multi-tiered problems, where you factor out a GCF then more factoring can be done
Remember: If there is a plus in the back, it’s the Wendy’s double Stack
1) GCF: 1) 12x4 + 8x3
2) 36x6y8z2 – 9x3y5z 3) 28x – 16x2
4) 64x8y4 + 40x6y12
5) 3xy6 – 6x4y5 + 2x8y3
2) Difference of Perfect Squares: 6) x2 – 16 7) 9x2 – 25
8) 25x2 – 64
9) 1 – x2
10) –81x2 + 4
11) – 49 + 16x2
12) x2 + 1
3) Perfect Square Trinomials: 13) 9x2 +24x + 16
14) x2 – 2x + 1 15) 16x2 + 8x + 1 16) 81x2 – 90x + 25
17) 25x2 + 60x + 36
18) 64x2 – 144x + 81
4) Trinomials: 19) x2 + 3x + 2 20) x2 – x – 20
21) x2 +4x – 21
22) x2 – 10x + 16
23) 6x2 +x – 1
24) 8x2 – 10x – 3 25) 5x2 – 20x + 12
26) 6x2 + 29x – 5
2
2
27) 7x – 5x – 2
28) 15x – 16x + 4
5) MULTI – TIERED
3
29) 3x – 3x
30) 5x4 – 20x2
31) 3x5 – 3x
32) 54x5 – 24x3
33) 4x3 + 24x2 + 36x 34) 12x5 – 60x4 + 75x3
Factoring Checklist Practice
Step 1: check for a GCF…always do this first.
 After factoring out a gcf (if there is one) proceed to step 2
Step 2: How many terms are there in expression (after factoring out the GCF)
2 terms
3 terms
Check to see if it’s the difference of perfect squares
Check to see if it’s a perfect square trinomial
2
2
2
2
X –9
–4x + 100
36x – 25y
x2 + 10x + 25
9x2 – 24x + 16
81x2 – 18x + 1
A perfect square minus a perfect square
1st and third terms are perfect squares, middle term is twice
The product of the square roots
YES: factor as 2 quantities:
YES: factor as 2 identical quantities,
(square root + square root)( square root – square root)
(square root + square root) choose sign of middle term
NO: Finished
NO: Multiply 1st term and third terms. Find factors of
The product that either + or – to get the middle term,
If you ever have x2 + 9, the expression is prime
sign of the third term tells you whether you should + or –
Re-write Polynomial so that it has four terms and group.
If this doesn’t work, the expression is prime
Watch for Multi-tiered problems, where you factor out a GCF then more factoring can be done
Remember: If there is a plus in the back, it’s the Wendy’s double Stack
1) GCF: 1) 12x4 + 8x3
2) 36x6y8z2 – 9x3y5z 3) 28x – 16x2
4) 64x8y4 + 40x6y12
5) 3xy6 – 6x4y5 + 2x8y3
2) Difference of Perfect Squares: 6) x2 – 16 7) 9x2 – 25
8) 25x2 – 64
9) 1 – x2
10) –81x2 + 4
11) – 49 + 16x2
12) x2 + 1
3) Perfect Square Trinomials: 13) 9x2 +24x + 16
14) x2 – 2x + 1 15) 16x2 + 8x + 1 16) 81x2 – 90x + 25
17) 25x2 + 60x + 36
18) 64x2 – 144x + 81
4) Trinomials: 19) x2 + 3x + 2 20) x2 – x – 20
21) x2 +4x – 21
22) x2 – 10x + 16
23) 6x2 +x – 1
24) 8x2 – 10x – 3 25) 5x2 – 20x + 12
26) 6x2 + 29x – 5
27) 7x2 – 5x – 2
28) 15x2 – 16x + 4
5) MULTI – TIERED
29) 3x3 – 3x
30) 5x4 – 20x2
31) 3x5 – 3x
32) 54x5 – 24x3
33) 4x3 + 24x2 + 36x 34) 12x5 – 60x4 + 75x3
KEY
1) 4x3(3x + 2)
2) 9x3y5z(4x3y3z – 1) 3) 4x(7 – 4x)
4) 8x6y4(8x2 + 5y8)
5) xy3(3y3 – 6x3y2 + 2x7)
6) (x + 4)(x – 4)
7) (3x + 5)(3x– 5)
8) (5x + 8)(5x – 8)
9) (1 +x)(1 – x)
10) (-9x + 2)( 9x + 2)
11) (-7 + 4x)(7 + 4x) 12) prime 13) (3x + 4)2 14) (x – 1)(x – 1)
15) (4x + 1)(4x + 1)
16) (9x – 5)2
2
2
17) (5x + 6)
18) (8x – 9)
19) (x + 2)(x + 1)
20) (x – 5)(x + 4)
21) (x + 7)(x – 3) 22) (x – 8)(x – 2)
23) (2x + 1)(3x – 1)
24) (4x + 1)(2x – 3) 25) (5x – 3)(x – 4) 26) (6x – 1)(x + 5) 27) (7x + 2)(x – 1) 28) (3x – 2)(5x – 2)
2
2
3
29) 3x(x +1)(x – 1)
30) 5x (x+2)(x – 2) 31) 3x(x +1)(x+1)(x–1) 32) 6x (3x +2)(3x –2) 33) 4x(x+ 3)(x + 3)
34) 3x3(2x–5)(2x–5)
KEY
1) 4x3(3x + 2)
2) 9x3y5z(4x3y3z – 1) 3) 4x(7 – 4x)
4) 8x6y4(8x2 + 5y8)
5) xy3(3y3 – 6x3y2 + 2x7)
6) (x + 4)(x – 4)
7) (3x + 5)(3x– 5)
8) (5x + 8)(5x – 8)
9) (1 +x)(1 – x)
10) (-9x + 2)( 9x + 2)
11) (-7 + 4x)(7 + 4x) 12) prime 13) (3x + 4)2 14) (x – 1)(x – 1)
15) (4x + 1)(4x + 1)
16) (9x – 5)2
2
2
17) (5x + 6)
18) (8x – 9)
19) (x + 2)(x + 1)
20) (x – 5)(x + 4)
21) (x + 7)(x – 3) 22) (x – 8)(x – 2)
23) (2x + 1)(3x – 1)
24) (4x + 1)(2x – 3) 25) (5x – 3)(x – 4) 26) (6x – 1)(x + 5) 27) (7x + 2)(x – 1) 28) (3x – 2)(5x – 2)
29) 3x(x +1)(x – 1)
30) 5x2(x+2)(x – 2) 31) 3x(x2 +1)(x+1)(x–1) 32) 6x3 (3x +2)(3x –2) 33) 4x(x+ 3)(x + 3)
3
34) 3x (2x–5)(2x–5)
KEY
1) 4x3(3x + 2)
2) 9x3y5z(4x3y3z – 1) 3) 4x(7 – 4x)
4) 8x6y4(8x2 + 5y8)
5) xy3(3y3 – 6x3y2 + 2x7)
6) (x + 4)(x – 4)
7) (3x + 5)(3x– 5)
8) (5x + 8)(5x – 8)
9) (1 +x)(1 – x)
10) (-9x + 2)( 9x + 2)
11) (-7 + 4x)(7 + 4x) 12) prime 13) (3x + 4)2 14) (x – 1)(x – 1)
15) (4x + 1)(4x + 1)
16) (9x – 5)2
17) (5x + 6)2
18) (8x – 9)2 19) (x + 2)(x + 1)
20) (x – 5)(x + 4)
21) (x + 7)(x – 3) 22) (x – 8)(x – 2)
23) (2x + 1)(3x – 1)
24) (4x + 1)(2x – 3) 25) (5x – 3)(x – 4) 26) (6x – 1)(x + 5) 27) (7x + 2)(x – 1) 28) (3x – 2)(5x – 2)
29) 3x(x +1)(x – 1)
30) 5x2(x+2)(x – 2) 31) 3x(x2 +1)(x+1)(x–1) 32) 6x3 (3x +2)(3x –2) 33) 4x(x+ 3)(x + 3)
34) 3x3(2x–5)(2x–5)
KEY
1) 4x3(3x + 2)
2) 9x3y5z(4x3y3z – 1) 3) 4x(7 – 4x)
4) 8x6y4(8x2 + 5y8)
5) xy3(3y3 – 6x3y2 + 2x7)
6) (x + 4)(x – 4)
7) (3x + 5)(3x– 5)
8) (5x + 8)(5x – 8)
9) (1 +x)(1 – x)
10) (-9x + 2)( 9x + 2)
11) (-7 + 4x)(7 + 4x) 12) prime 13) (3x + 4)2 14) (x – 1)(x – 1)
15) (4x + 1)(4x + 1)
16) (9x – 5)2
2
2
17) (5x + 6)
18) (8x – 9)
19) (x + 2)(x + 1)
20) (x – 5)(x + 4)
21) (x + 7)(x – 3) 22) (x – 8)(x – 2)
23) (2x + 1)(3x – 1)
24) (4x + 1)(2x – 3) 25) (5x – 3)(x – 4) 26) (6x – 1)(x + 5) 27) (7x + 2)(x – 1) 28) (3x – 2)(5x – 2)
2
2
3
29) 3x(x +1)(x – 1)
30) 5x (x+2)(x – 2) 31) 3x(x +1)(x+1)(x–1) 32) 6x (3x +2)(3x –2) 33) 4x(x+ 3)(x + 3)
34) 3x3(2x–5)(2x–5)
KEY
1) 4x3(3x + 2)
2) 9x3y5z(4x3y3z – 1) 3) 4x(7 – 4x)
4) 8x6y4(8x2 + 5y8)
5) xy3(3y3 – 6x3y2 + 2x7)
6) (x + 4)(x – 4)
7) (3x + 5)(3x– 5)
8) (5x + 8)(5x – 8)
9) (1 +x)(1 – x)
10) (-9x + 2)( 9x + 2)
11) (-7 + 4x)(7 + 4x) 12) prime 13) (3x + 4)2 14) (x – 1)(x – 1)
15) (4x + 1)(4x + 1)
16) (9x – 5)2
17) (5x + 6)2
18) (8x – 9)2 19) (x + 2)(x + 1)
20) (x – 5)(x + 4)
21) (x + 7)(x – 3) 22) (x – 8)(x – 2)
23) (2x + 1)(3x – 1)
24) (4x + 1)(2x – 3) 25) (5x – 3)(x – 4) 26) (6x – 1)(x + 5) 27) (7x + 2)(x – 1) 28) (3x – 2)(5x – 2)
29) 3x(x +1)(x – 1)
30) 5x2(x+2)(x – 2) 31) 3x(x2 +1)(x+1)(x–1) 32) 6x3 (3x +2)(3x –2) 33) 4x(x+ 3)(x + 3)
3
34) 3x (2x–5)(2x–5)
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