Question

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Answer 1

$$\frac{f(x)+1}{x+2}=\frac{f(x)}{x+2}+\frac1{x+2}=\dots+\frac3{x+2}+\frac1{x+2}=\frac4{x+2}$$so our remainder is \(4\)

Answer 2

Alternatively, the *polynomial remainder theorem* tells us the remainder after division of \(f(x)\) by \(x-a\) is just \(f(a)\) -- which is intuitive.
http://en.wikipedia.org/wiki/Polynomial_remainder_theorem

Answer 3

therefore we're given $$f(-2)=3$$ and are asked to find \(f(-2)+1=3+1=4\)

Answer 4

just wat i was bout to say! ahah gd work.