Q. 2 C4.4( 9 Votes )
Use the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases:
f(x) = x3 – 4x2 + x + 6, g(x) = x – 2
Answer :
By Factor Theorem, we know that,
If p(x) is a polynomial and a is any real number, then g(x) = (x – a) is a factor of p(x), if p(a) = 0
For checking (x – 2) to be a factor, we will find f(2)
⇒ f(2) = (2)3 – 4(2)2 + (2) + 6
⇒ f(–1) = 8 – 16 + 2 + 6
⇒ f(–1) = 0
As, f(–1) is equal to zero, therefore, g(x) = (x – 2) is a factor of f(x)
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