Question

f(x)=5x³+x²-5x-1,g(x)=x+1 ,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 if

degree one or more than one

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) = 5x³ + x² - 5x - 1 ,

g(x) = x + 1 ,

g(x) = 0 ,

=> x + 1 = 0

=> x = -1

Therefore ,

Zero of g(x) is -1 ,

Now ,

F(-1) = 5(-1)³ + (-1)² - 5(-1) - 1

= -5 + 1 + 5 - 1

=-6 + 6

= 0

Therefore ,

By Factor theorem ,

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

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