How do you use the remainder theorem to find the remainder for the division (x^4+5x^3-14x^2)div(x-2)(x4+5x3−14x2)÷(x−2)?

1 Answer
EZ as pi
Sep 8, 2016

f(2) = 0f(2)=0 There is no remainder.
x-2x−2 is a factor.

Explanation:

If we have f(x) = x^4 +5x^3-14x^2f(x)=x4+5x3−14x2

Let x-2 = 0 rarr x =2x−2=0→x=2

The remainder of x^4 +5x^3-14x^2 div(x-2)x4+5x3−14x2÷(x−2)
is found from f(2)f(2)

f(2) = 2^4 +5(2)^3-14(2)^2f(2)=24+5(2)3−14(2)2

= 16+40-56 =016+40−56=0

The fact that the remainder is 0, (ie there is no remainder), means that (x-2)(x−2) is a factor of x^4 +5x^3-14x^2x4+5x3−14x2

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