SOLUTION: Use the remainder theorem to find the remainder when f(x) is divided by g(x) F(x)=x^4+8x^3+12x^2; g(x)=x+1

Algebra ->  Expressions-with-variables -> SOLUTION: Use the remainder theorem to find the remainder when f(x) is divided by g(x) F(x)=x^4+8x^3+12x^2; g(x)=x+1      Log On


   



Question 761868: Use the remainder theorem to find the remainder when f(x) is divided by g(x)
F(x)=x^4+8x^3+12x^2; g(x)=x+1

Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Given expression F(x)is x%5E4%2B8%2Ax%5E3%2B12%2Ax%5E2
Remainder theorem - if when a function f(x) is divided by (x-a), the remainder is f(a) - that is, the remainder is the value of the function when you substitute x with a.
Here we are dividing by g(x) = x + 1. Comparing it with (x-a) form, a = -1.
So remainder = F(-1) =
(Putting x = -1 in the expression F(x))

%28-1%29%5E4+%2B+8%2A%28-1%29%5E3+%2B+12%2A%28-1%29%5E2
=
1+%2B+8%2A%28-1%29+%2B+12%2A%281%29
=
1+-+8+%2B+12+=+5
Remainder when F(x) is divided by (x+1) is highlight%285%29
:)