1.

f(x)=x³+3x²+3x+1,g(x)=x+1,Use the Factor Theorem to determine whether g(x) is factor of f(x) in each cases.

Answer»

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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 + 3x² + 3X + 1 ,


G(x) = x + 1 ,


g(x) = 0


=> x + 1 = 0


=> x = -1 ,


Therefore ,


ZERO of g(x) is -1.


Now ,


F(-1) = (-1)³ + 3(-1)² + 3(-1) + 1


= -1 + 3 - 3 + 1


= -4 + 4


= 0


Therefore ,


By Factor theorem ,


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


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