Question

factor each given polynomial and drag the correct solution next to the polynomial. not all choices will be used.
$(6x+5)(6x-5)$
$x^{2}+16x+64$
$(3x+7)(3x-7)$
$(x+11)(x-11)$
$36x^{2}-25$
$(x+8)(x-8)$
$(3x-1)^{2}$
$9x^{2}-49$
$(3x-7)^{2}$
$(x+8)^{2}$
$9x^{2}+6x+1$
$(6x-5)^{2}$
$(x-11)^{2}$
$x^{2}-22x+121$
$(3x+1)^{2}$

Explanation:

Step1: Match difference of squares

Recall $a^2-b^2=(a+b)(a-b)$

• $36x^2-25=(6x)^2-5^2=(6x+5)(6x-5)$
• $9x^2-49=(3x)^2-7^2=(3x+7)(3x-7)$

Step2: Match perfect square trinomials

Recall $(a\pm b)^2=a^2\pm2ab+b^2$

• $x^2+16x+64=(x+8)^2$
• $9x^2+6x+1=(3x+1)^2$
• $x^2-22x+121=(x-11)^2$

Answer:

• $36x^2 - 25

ightarrow (6x + 5)(6x - 5)$

• $9x^2 - 49

ightarrow (3x + 7)(3x - 7)$

• $x^2 + 16x + 64

ightarrow (x + 8)^2$

• $9x^2 + 6x + 1

ightarrow (3x + 1)^2$

• $x^2 - 22x + 121

ightarrow (x - 11)^2$