Question

f(x)=x³-4x²+x+6, g(x)=x-2,Use the Factor Theorem to determine whether g(x) is factor of f(x) in each cases.

Answer 1

yes g(x) is a factor of p(x)

Answer 2

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Factor Theorem :

Let p(x) be a polynomial of

degree one or more than 1 and

a is a real number .Then

i ) x-a , will be a factor of p(x) if

p(a) = 0 conversely ,

ii ) If x - a is a factor of p(x) ,

then p(a) = 0

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Here ,

F(x) = x³ - 4x² + x + 6 ,

g(x) = x - 2

g(x) = 0

=> x - 2 = 0

=> x = 2

Therefore ,

Zero of g(x) is 2 ,

Now ,

p(2) = 2³ - 4(2)² +2 + 6

= 8 - 16 + 2 + 6

= 16 - 16

= 0

Therefore ,

By Factor theorem ,

g(x ) is a factor of f(x).

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