Could you please explain #10 no calculator practice test 9

My apologies that this sat in my inbox for a few days! Summer, ya know?

The key to this question is remembering that the corresponding coefficients of equivalent polynomials will be equal. Let’s look at the given equation:

The left side isn’t in expanded form but once it is, we know that the coefficients of the terms on each side will be equal, and the coefficients of the terms will be equal, etc. So let’s expand.

Now figure out the coefficients of each power of …

Here’s where we get to apply the rule I linked to above. We now know that:

,

,

,

and of course .

The first equation gives us , use either of the other two to solve for :

Now that you know and , you know .