Question

f(x)=4x³+20x²+33x+18,g(x)=2x+3,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

Solution :

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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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Given

f(x) = 4x³ + 20x² + 33x + 18 ,

g(x) = 2x + 3 ,

g(x) = 0

=> 2x + 3 = 0

=> x = -3/2

Now , f( -3/2 )

= 4(-3/2)³ + 20(-3/2)² + 33(-3/2) + 18

= 4(-27/8) + 20(9/4) - 33(3/2 ) + 18

= -27/2 + 5 × 9 - 99/2 + 18

= ( -27 - 99 )/2 + 45 + 18

= - 126/2 + 63

= - 63 + 63

= 0

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