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What does the remainder theorem conclude given that [tex]\frac{f(x)}{x+6}[/tex] has a remainder of 14? f(?) = ? Please help this is literally all the information I was given and I've tried to figure it out so many different ways and it's just not working.

Respuesta :

Answer:

[tex]f(-6)=14[/tex]

Step-by-step explanation:

The remainder theorem tells us that If a polynomial f(x) is divided by a linear factor, L(x)=x-a, the remainder of the quotient is f(a).

In this case:

f(x) divided by x+6 has a remainder of 14.

  • The Polynomial =f(x)
  • Linear Factor = x+6

Comparing the linear factor with x-a, we have:

[tex]x+6=x-(-6)[/tex]

Therefore the remainder of the quotient:

[tex]f(-6)=14[/tex]

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