Question

factoring expressions
factor the expression using gcf.
① 9 + 21
② 32 + -48
③ 8x + 2
④ 3y - 24
⑤ 20z - 8
⑥ 36a + 16b

Explanation:

Step1: Find GCF of 9 and 21

Factors of 9: 1, 3, 9; Factors of 21: 1, 3, 7, 21. GCF = 3

Step2: Factor out GCF from $9+21$

$3\times(3 + 7)$

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Step1: Find GCF of 32 and 48

Factors of 32: 1,2,4,8,16,32; Factors of 48:1,2,3,4,6,8,12,16,24,48. GCF = 16

Step2: Factor out GCF from $32+(-48)$

$16\times(2 - 3)$

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Step1: Find GCF of 8 and 2

Factors of 8:1,2,4,8; Factors of 2:1,2. GCF = 2

Step2: Factor out GCF from $8x+2$

$2\times(4x + 1)$

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Step1: Find GCF of 3 and 24

Factors of 3:1,3; Factors of 24:1,2,3,4,6,8,12,24. GCF = 3

Step2: Factor out GCF from $3y-24$

$3\times(y - 8)$

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Step1: Find GCF of 20 and 8

Factors of 20:1,2,4,5,10,20; Factors of 8:1,2,4,8. GCF = 4

Step2: Factor out GCF from $20z-8$

$4\times(5z - 2)$

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Step1: Find GCF of 36 and 16

Factors of 36:1,2,3,4,6,9,12,18,36; Factors of 16:1,2,4,8,16. GCF = 4

Step2: Factor out GCF from $36a+16b$

$4\times(9a + 4b)$

Answer:

1. $3(3+7)$
2. $16(2-3)$
3. $2(4x+1)$
4. $3(y-8)$
5. $4(5z-2)$
6. $4(9a+4b)$