Hi Mike… can you work through the steps to solve Q 24 from Official Test 9 Section 4? thanks!

Sure thing. Remember that when you have an defined and then you’re asked about something like , you plug that WHOLE thing in parentheses (called the argument) into the original function where was. Like so:

Once you’ve expanded it, remember that corresponding coefficients in equal polynomials are equal. So because we know the above is equivalent to , we know that the terms are equal: , and that the constant terms are equal .

To get the value of , let’s solve the equation *without* an term, to avoid having to wonder whether we need the positive or negative root (spoiler alert: both are answer choices).