Algebra
ANSWER KEY
5C2: Factoring Polynomials A
1. x² – 7x + 10 =
(x – 5) (x – 2)
GCF = 1
A∙C = 10; B = -7
-5 & -2
x² – 7x + 10
x² – 5x – 2x + 10
x(x – 5) – 2(x – 5)
2. x² + 3x + 2 =
(x + 1) (x + 2)
GCF = 1
A∙C = 2; B = 3
1&2
x² + 3x + 2
x² + x + 2x + 2 x(x
+ 1) + 2(x + 1)
3. x² – x – 20 =
(x – 5) (x + 4)
GCF = 1
A∙C = -20; B = -1
-5 & 4
x² – x – 20
x² – 5x + 4x – 20
x(x – 5) + 4(x – 5)
4. x² + 4x – 5 =
(x + 5) (x – 1)
GCF = 1
A∙C = -5; B = 4
5 & -1
x² + 4x – 5
x² + 5x – x – 5 x(x
+ 5) – 1(x + 5)
5. 2x² + 5x – 12 =
(x + 4) (2x – 3)
GCF = 1
A∙C = -24; B = 5
8 & -3
2x² + 5x – 12
2x² + 8x – 3x – 12
2x(x + 4) – 3(x + 4)
6. 3x² + 17x – 6 =
(3x – 1) (x + 6)
GCF = 1
A∙C = -18; B = 17
-1 & 18
3x² + 17x – 6
3x² – x + 18x – 6
x(3x – 1) + 6(3x – 1)
7. x² – 2x – 15 =
(x – 5) (x + 3)
GCF = 1
A∙C = -15; B = -2
-5 & 3
x² – 2x – 15
x² – 5x + 3x – 15
x(x – 5) + 3(x – 5)
8. 6x² – 10x + 4 =
2 (x – 1) (3x – 2)
GCF = 2
A∙C = 6; B = -5
-3 & -2
2 [ 3x² – 5x + 2 ]
2 [ 3x² – 3x – 2x + 2 ]
2 [ 3x(x – 1) – 2(x – 1) ]
9. 7x² + 12x – 4 =
(7x – 2) (x + 2)
GCF = 1
A∙C = -28; B = 12
-2 & 14
7x² + 12x – 4
7x² – 2x + 14x – 4
x(7x – 2) + 2(7x – 2)
10. 80x² – 118x + 42 =
2 (5x – 3) (8x – 7)
GCF = 2
A∙C = 840; B = -59
-24 & -35
2 [ 40x² – 59x + 21 ]
2 [ 40x² – 24x – 35x + 21 ]
2 [ 8x(5x – 3) – 7(5x – 3) ]
11. 42x² + 55x + 8 =
(7x + 8) (6x + 1)
GCF = 1
A∙C = 336; B = 55
48 & 7
42x² + 55x + 8
42x² + 48x + 7x + 8
6x(7x + 8) + 1(7x + 8)
12. x² – 15x + 56 =
(x – 7) (x – 8)
GCF = 1
A∙C = 56; B = -15
-7 & -8
x² – 15x + 56
x² – 7x – 8x + 56
x(x – 7) – 8(x – 7)
13. 20x² + 62x + 30 =
2 (5x + 3) (2x + 5)
GCF = 2
A∙C = 150; B = 31
6 & 25
2 [ 10x² + 31x + 15 ]
2 [ 10x² + 6x + 25x + 15 ]
2 [ 2x(5x + 3) + 5(5x + 3) ]
14. 30x² + 84x + 54 =
6 (x + 1) (5x + 9)
GCF = 6
A∙C = 45; B = 14
5&9
6 [ 5x² + 14x + 9 ]
6 [ 5x² + 5x + 9x + 9 ]
6 [ 5x(x + 1) + 9(x + 1) ]
15. 36x² – 35x – 11 =
(4x + 1) (9x – 11)
GCF = 1
A∙C = -396; B = -35
9 & -44
36x² – 35x – 11
36x² + 9x – 44x – 11
9x(4x + 1) – 11(4x + 1)