Question

When f(x) is divided by x+2, the quotient is x^2+4x-7+8/x+2. What is f(-2)

Answer 1

taking a peek at the division, it looks like

`\cfrac{f(x)}{x+2}\implies x^2+4x-7+\cfrac{8}{x+2}\impliedby \begin{cases} \stackrel{ \textit{\small quotient} }{x^2+4x-7}\\\\ \stackrel{\textit{\small remainder}}{8} \end{cases}`

so what's f( -2 )?

well, if take a looksie at the remainder theorem, whenever we have a division by some form of (x - a) if we divide a polynomial by "a" our remainder will be the same value as f(a).

what the hell all that means?

well, it means that for this case x + 2, we can rewrite as ( x - (-2) ), such that if we divide f(x) by (x+2), it's going to be give a remainder that's the same as f( -2 ). wait a second!!! we already know the remainder from above, it was "8", so f( -2 ) = 8.