Factor Practice #2
Name___________________
Factoring Steps:
1) Write in descending order.
A polynomial that does not
2) Factor out GCF (including -1)
factor is known as prime
3) Determine number of terms:
a) Binomial -> Difference of two squares -> (a2 – b2) => (a-b)(a+b)
1. x2 – 25
(x+5)(x-5)
2. x2 – 81
(x+9)(x-9)
3. –1 + x2
(x-1)(x+1)
4. –x3 - 4x
-x(x2 + 4)
5. -2x3 + 2x
-2x(x+1)(x-1)
6. 25x2 – 9
(5x+3)(5x-3)
7. 36a − 9
9(4a – 1)
8. 400 − 36v2
-4(3v+10)(3v-10)
9. 10p3 − 1960p
10p(p+14)(p-14)
10. 81v4 − 900v2
9v2(3v-10)(3v+10)
11. -12x2 - 3x3
-3x2(x+4)
12. 49x2 + 100
Prime
13. 2x6 + 20x4 - 4x5
2x4(x2 – 2x + 10)
14. 28v3 + 16v2 − 21v − 12
Prime
15. 81a2 – 9b2
9(3a-b)(3a+b)
16. x2 – 9
(x-3)(x+3)
17. 16x2 - 9
(4x-3)(4x+3)
18. 49x2 - 64
(7x-8)(7x+8)
19. 13x2 - 130x
13x(x-10)
20. x2 – 121
(x-11)(x+11)
21. 4m2 − 25
(2m-5)(2m+5)
22. k4 − 36
(k2-6)(k2+6)
23. 1 − r2
-(r-1)(r+1)
24. 343b2 − 7b4
-7b2(b+7)(b-7)
25. n8 − 256
(n4+16)(n2+4)(n+2)(n-2)
26. 49n2 − 56n + 16
Prime
27. -6x3 + 8x
-2x(3x2 - 4)
28. -33x2 - 330x
-33x(x+10)
29. 54n2 − 105n + 63n3 − 90
3(21n3 + 18n2 – 35n – 30)
30. -81b2 – 9a2
-9(a2+9b2)
Factor Practice #3
Factoring Steps:
1) Write in descending order
2) Factor out GCF (including –1)
3) Determine number of terms:
a) Binomial -> Diff. of 2 squares
b) 4 or more terms -> Grouping
Name___________________
A polynomial that does not
factor is known as ________
1. 8r3 − 64r2 + r − 8
2. − 5 + 12x3 − 30x + 2x2
( 8r2 + 1 ) ( r − 8 )
3. 25v3 + 5v2 + 30v + 6
( 2x2 − 5 ) ( 6x + 1 )
4. 4v3 − 12v2 − 5v + 15
( 5v2 + 6 ) ( 5v + 1 )
5. −56p − 35 + 24p3 + 15p2
( 4v2 − 5 ) ( v − 3 )
6. 63n3 + 54n2 − 105n − 90
( 3p2 − 7 ) ( 8p + 5 )
7. 6 + 30v + 5v2 + 25v3
3( 3n2 − 5 ) ( 7n + 6 )
8. 4 xy + 6 − x − 24 y
( 5v2 + 6 ) ( 5v + 1 )
9. 12x2u + 3x2v + 28yu + 7yv
(x −6)(4y −1)
10. 28xy + 25 + 35x + 20y
( 3x2 + 7y ) ( 4u + v)
11. 25a8 - 100b4
( 7x + 5 ) ( 4y + 5 )
12. 21y6z – 49y5z – 14y7z
25( a4 – 2b2 )( a4 + 2b2)
13. 15a2z − 12a2c + 45xz − 36xc
-7y5z( 2y2 – 3y + 7)
14. -72a3 + 36a5 + 36a2 – 18a4
-3( a2 + 3x ) ( 4c − 5z )
18a2( a2 – 2 )( 2a – 1 )
Factor Practice #4
Name___________________
Factoring Steps:
1) Write in descending order
A polynomial that does not
2) Factor out GCF (neg 1)
factor is known as prime
3) Determine number of terms:
a) Binomial -> Diff. of 2 squares
b) 4 or more terms -> Grouping
c) Trinomial -> Leading Coefficient of 1:
Check for perfect square trinomial -> a2  2ab + b2
Product/Sum: x2 + bx + c = ( x + )( x + )
x2 - bx + c = ( x - )( x - )
x2  bx - c = ( x + )( x - )
Leading Coefficient other than 1:
1. x2 - 5x - 84
2. x2 - 16x + 64
3. x2 + 13x + 36
(x + 7)(x - 12)
4. x2 - 10x + 25
(x - 8)2
5. x2 - 13x + 12
(x + 9)(x + 4)
6. x2 + 4x - 32
(x - 5)2
7. x2 - 8x + 16
(x - 1)(x - 12)
8. 2x + x2 - 8
(x - 4)(x + 8)
9. -20x + x2 + 100
(x - 4)2
10. 36 - 12x + x2
(x - 2)(x + 4)
11. x2 + 84 - 19x
(x - 10)2
12. 9x + x2 + 8
(x - 6)2
13. 24 + x2 - 10x
(x - 12)(x - 7)
14. – 8 + x2 - 7x
(x + 8)(x + 1)
15. – 10 - 9x + x2
(x - 4)(x - 6)
16. −44n + 40 + 4n2
(x - 8)(x + 1)
17. -4n2 - 16n + 48
(x - 10)(x + 1)
18. -32b - 2b2 - 128
4(n − 10)(n − 1)
19. 3m2 − 72 + 6m
-4(n − 2)(n + 6)
20. 200 − 65k + 5k2
-2(b + 8)2
21. 2n2 − 108 + 6n
3(m + 6)(m − 4)
5(k − 5)(k − 8)
2(n + 9)(n − 6)
22. 10n2 + 250 + 100n
23. 63m – 72 + 18m2
10(n + 5)2
24. –x2y2 – 25x2 + 4y2 + 100
9(2m2 + 7m – 8)
25. 256 – z20
-(x-2)(x+2)(y2 + 25)
-(z10+16)(z5+4)(z5-4)
26. 20m – 40n -8n2 + 4mn
27. t2 + 20t – 6t - 150 + t2 + 30
4(m-2n)(n+5)
2(t-5)(t+12)
Factor Practice #5
Name___________________
Factoring Steps:
1) Write in descending order
A polynomial that does not
2) Factor out GCF (neg 1)
factor is known as prime
3) Determine number of terms:
a) Binomial -> Diff. of 2 squares
b) 4 or more terms -> Grouping
c) Trinomial -> Leading Coefficient of 1:
Check for perfect square trinomial -> a2  2ab + b2
Product/Sum: x2 + bx + c = ( x + )( x + )
x2 - bx + c = ( x - )( x - )
x2  bx - c = ( x + )( x - )
Leading Coefficient other than 1:
Check for perfect square trinomial
ax2  bx  c
1. 2v2 + 11v + 5
2. 49x2 - 42x + 9
(2v + 1)(v + 5)
3. −6 + 15n2 − 27n
(7x - 3)2
4. −15n + 4n2 − 25
3(5n + 1)(n − 2)
5. 4n2 + 4 − 17n
(n − 5)(4n + 5)
6. 6x2 + 6 + 37x
(n − 4)(4n − 1)
7. −12 + 10n + 12n2
(x + 6)(6x + 1)
8. -15n2 – 20 + 40n
-5(3n − 2)(n − 2)
2(2n + 3)(3n − 2)
9. -159a - 21a2 - 84
10. 9x4 - 60x2 + 100
(3x2 - 10)2
-3(7a + 4)(a + 7)
11. 7x2 – 175 – x3 + 25x
12. 49x4 + 112x2 + 64
(7x2 + 8)2
-(x - 7)(x + 5)(x – 5)