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Synthetic Division of Polynomials

If fx+2=x2+...

Question

If $f (x + 2) = x^{2} + 7 x - 13$ , then find the remainder when $f (x)$ is divided by $(x + 2)$ .

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Solution

$f (x + 2) = x^{2} + 7 x - 13$

The remainder, when $f (x)$ is divided by $(x + 2)$ is $f (- 2)$ .

Put $x = - 4$ in the given equation.

$f (- 4 + 2) = (- 4)^{2} + 7 (- 4) - 13$

$f (- 2) = 16 - 28 - 13 = - 25$

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