College Board Test 4, Math 4 #25 (the explanation link that you previously made does not work)

College Board Test 4, Math 4 #25 (the explanation link that you previously made does not work)

Huh…that’s so weird. Sure enough, though, that post seems to have gotten deleted somehow!

So, here we go again!

The key is recognizing how the given functions are similar.

$f(x)=2x^3+6x^2+4x\\g(x)=x^2+3x+2$

How about if we rewrite $f(x)$ like this:

$f(x)=2x\left(x^2+3x+2\right)$

That makes things a little clearer, right? So we know that $f(x)=2x\times g(x)$ .

Do a little substitution into the answer choices and you should see which one is divisible by $2x+3$ :

A) $2x\times g(x) + g(x)$ <– nah

B) $2x\times g(x) + 3g(x)$ <– YES!!!

C) $2\left(2x\times g(x)\right) + 3g(x)$ <– nope

D) $3\left(2x\times g(x)\right)+2g(x)$ <–nuh-uh

To be super clear, choice B works because it can be factored like this:

$2x\times g(x) + 3g(x)=(2x+3)\times g(x)$

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