Question

F(x) = 5x + x2 - 5x - 1, g(x)= x + 1​

Answer 1

Answer:

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