Question

f(x)=3x³+x²-20x+12, g(x)=3x-2,Use the Factor Theorem to determine whether g(x) is factor of f(x) in each cases.

Answer 1

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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 - q , 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) = 3x³ + x² -20x + 12,

g(x) = 3x - 2 ,

g(x) = 0

=> 3x - 2 = 0

=> x = 2/3

Zero of g(x) = 2/3 ,

Now ,

F(2/3) = 3(2/3)³+(2/3)²-20(2/3)+12

= 3(8/27) + 4/9 - 40/3 + 12

= 8/9+4/9-40/3+12

= 12/9 - 40/3 + 12

= 4/3-40/3 + 12

= -36/3 + 12

= -12 + 12

= 0

By factor Theorem , g(x) is a

factor of f(x)

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