Question

Verify, whether g(x)is a factor of f (x)
i) f (x)= x - 3x² + 4x - 4, (x) = x - 2
ii) f(x) = 2x + 4x+6, g(x) = x+1
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Answer 1

Answer:

Given polynomial f(x)=x

3

−4x

2

+x+6 the factor of g(x)=x−2

If x-2 is factor then x-2=0 or x=2

Replace x in p(x) by 2 we get

f(x)=x

3

−4x

2

+x+6

f(2)=(2)

3

−4(2)

2

+(2)+6

⇒f(2)=8−16+2+6

⇒f(2)=0

So f(x) is zero by g(x) =x-2 then g(x)=(x-2) is factor of f(x)=x

3

−4x

2

−x+6