Question

f(x)=5x^{3}+x^{2}-5x-1,g(x)=x+1
f(x)=x^{3}+3x^{2}+3x+1,g(x)=x+1
use factor therom to determine wether g of x if a factor of f of x​

Answer 1

Answer:

Solution

verified

Verified by Toppr

Given polynomial f(x)=5x

3

+x

2

−5x−1 the factor of g(x)=x+1

If x+1 is factor then x+1=0 or x=−1

Replace x in f(x) by −1 we get

f(x)=5x

3

+x

2

−5x−1 g(x)=x+1

f(−1)=5(−1)

3

+(−1)

2

−5(−1)−1

⇒f(−1)=−5+1+5−1

⇒f(−1)=0

So f(−1) is zero by g(x)=x+1 then g(x)=x+1 is factor of f(x)=5x

3

+x

2

−5x−1