Question

algebra 1
factoring with gcf
factor the common factor out of each expression.

1. $8 + 6x^4$
2. 2
3. $4n^9 + 12n$

4)

1. $-12a - 3$

6)

1. $12n^5 + 16n^3$

8)

1. $5k^2 - 40k + 10$
2. $-60 + 60n^2 + 50n^3$
3. $-36n^3 - 12n - 28$
4. $63n^3 + 81n + 18$
5. $-24a^2b^2 + 36ab - 60a$

Explanation:

Step1: Find GCF of 8 and 6

GCF(8,6)=2

Step2: Factor out GCF from $8+6x^4$

$2(4 + 3x^4)$

Step1: Find GCF of 4 and 12

GCF(4,12)=4; GCF($n^9,n$)=$n$

Step2: Factor out GCF from $4n^9+12n$

$4n(n^8 + 3)$

Step1: Find GCF of -12 and -3

GCF(12,3)=3; factor out -3

Step2: Factor out GCF from $-12a-3$

$-3(4a + 1)$

Step1: Find GCF of 12 and 16

GCF(12,16)=4; GCF($n^5,n^3$)=$n^3$

Step2: Factor out GCF from $12n^5+16n^3$

$4n^3(3n^2 + 4)$

Step1: Find GCF of 5, -40 and 10

GCF(5,40,10)=5

Step2: Factor out GCF from $5k^2-40k+10$

$5(k^2 - 8k + 2)$

Step1: Find GCF of -60, 60 and 50

GCF(60,60,50)=10; rearrange terms

Step2: Factor out GCF from $-60+60n^2+50n^3$

$10(5n^3 + 6n^2 - 6)$

Step1: Find GCF of -36, -12 and -28

GCF(36,12,28)=4; factor out -4

Step2: Factor out GCF from $-36n^3-12n-28$

$-4(9n^3 + 3n + 7)$

Step1: Find GCF of 63, 81 and 18

GCF(63,81,18)=9

Step2: Factor out GCF from $63n^3+81n+18$

$9(7n^3 + 9n + 2)$

Step1: Find GCF of -24, 36 and -60

GCF(24,36,60)=12; GCF($a^2b^2,ab,a$)=$a$; factor out -12a

Step2: Factor out GCF from $-24a^2b^2+36ab-60a$

$-12a(2ab^2 - 3b + 5)$

Answer:

1. $2(4 + 3x^4)$
2. $4n(n^8 + 3)$
3. $-3(4a + 1)$
4. $4n^3(3n^2 + 4)$
5. $5(k^2 - 8k + 2)$
6. $10(5n^3 + 6n^2 - 6)$
7. $-4(9n^3 + 3n + 7)$
8. $9(7n^3 + 9n + 2)$
9. $-12a(2ab^2 - 3b + 5)$