Question

name: _____________date:factoring binomialsn-gen math⁸ 7 homeworkfluency1. which of the following is not a common factor of the numbers 18 and 42?(1) 6(2) 2(3) 3(4) 72. which of the following is not a correct factorization of the binomial $12x + 30$?(1) $2(6x + 15)$(2) $3(4x + 10)$(3) $12(x + 18)$(4) $6(2x + 5)$3. if the binomial $8n + 20$ was written as an equivalent product of its greatest common factor and another binomial, which of the following would be the binomial in the product?(1) $2n + 5$(2) $5n + 7$(3) $n + 12$(4) $4n + 10$4. for each of the following binomials, identify its gcf and then write it as the product of its gcf with another binomial.(a) $6x + 30$gcf = ____factored form:(b) $14n + 49$gcf = ____factored form:(c) $16y - 8$gcf = ______factored form:

Explanation:

Step1: Find factors of 18,42

Factors of 18: $1,2,3,6,9,18$
Factors of 42: $1,2,3,6,7,14,21,42$
Common factors: $1,2,3,6$

Step2: Identify non-common factor

7 is not in common factors.

Step3: Verify factorization of $12x+30$

(1) $2(6x+15)=12x+30$, correct.
(2) $3(4x+10)=12x+30$, correct.
(3) $12(x+18)=12x+216
eq12x+30$, incorrect.
(4) $6(2x+5)=12x+30$, correct.

Step4: Factor $8n+20$

GCF of 8 and 20 is 4.
$8n+20=4(2n+5)$, so binomial is $2n+5$.

Step5: Factor $6x+30$

GCF of 6 and 30 is 6.
$6x+30=6(x+5)$

Step6: Factor $14n+49$

GCF of 14 and 49 is 7.
$14n+49=7(2n+7)$

Step7: Factor $16y-8$

GCF of 16 and 8 is 8.
$16y-8=8(2y-1)$

Answer:

1. (4) 7
2. (3) $12(x+18)$
3. (1) $2n+5$
4. (a) gcf = 6; factored form: $6(x+5)$

(b) gcf = 7; factored form: $7(2n+7)$
(c) gcf = 8; factored form: $8(2y-1)$