1 Answer

James Adams · Answer 1 · 2022-03-26T12:55:29+0000

Answer:

(x+2)(9x+6)

Explanation:

This is the whole process. Skip down to the bolded important part if you want.

Going to quickly expand it again:

$9x(x+2)+6(x+2)\\9x^2+18x+6x+12\\9x^2+24x+12$

This is in the form of:

ax^2+bx+c

To factor a trinomial in this form, you need to find 2 numbers that multiply together to make
, and also add together to make
.

In this case,

$ac=9*12=108\\b=24\\\\18*6=108=ac\\18+6=24=b$

those 2 numbers are 18 and 6.

Then, in the above, expanded equation, you need to split b into 2 numbers, from 24 into 18 and 6.

$9x^2+24x+12\\9x^2+18x+6x+12$

Then, split the equation in half and factor each half individually.

$(9x^2+18x)+(6x+12)\\9x(x+2)+6(x+2)$

Important part ==========

Now, we're right back at where we started with your question. All we need to do now is factor out the (x+2).

$9x(x+2)+6(x+2)\\(x+2)(9x+6)$

And you're done, that's all.

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