Respuesta :

sqdancefan

Answer:

  [tex]f(\boxed{-5})=\boxed{17}[/tex]

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.

Answer:

Step-by-s[tex]f(-5)=17[/tex]

tep explanation:

Let [tex]Q(x)[/tex] be the quotient of [tex]\frac{f(x)}{x+5}[/tex].

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

[tex]\frac{f(x)}{x+5}=Q(x)+\frac{R}{x+5}[/tex]

Multiply both sides by [tex](x+5)[/tex]:

[tex]f(x)=Q(x)(x+5)+R[/tex]

Substitute [tex]x=-5[/tex]:

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

[tex]f(-5)=Q(x)(0)+17[/tex]

[tex]f(-5)=17[/tex]

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