Question

Please help me with the question.

Answer 1

Answer:

Step-by-s$f(-5)=17$

tep explanation:

Let $Q(x)$ be the quotient of $\frac{f(x)}{x+5}$.

Let $R$ be the remainder. $R$ is a constant real number because we are dividing by a linear factor, $x+5$.

$\frac{f(x)}{x+5}=Q(x)+\frac{R}{x+5}$

Multiply both sides by $(x+5)$:

$f(x)=Q(x)(x+5)+R$

Substitute $x=-5$:

$f(-5)=Q(x)(-5+5)+17$  (We were given $R=17$ since they did say the remainder is 17.)

$f(-5)=Q(x)(0)+17$

$f(-5)=17$

Answer 2

Answer:

  $f(\boxed{-5})=\boxed{17}$

Step-by-step explanation:

The remainder theorem tells you that f(a) is the result of division of f(x) by (x-a).

Here, you have f(x)/(x+5) = 17, so a=-5 and f(-5) = 17.