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Question

Use the factor theorem to determine whether g(x) is a factor of f(x)

f(x)=22x2+5x+2;g(x)=x+2


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Solution

Checking whether g(x) is a factor of f(x) or not.

According to the factor theorem, if g(x)=(x-a) is a factor of f(x) then f(a)=0.

Here, f(x)=22x2+5x+2;g(x)=x+2

Now, substitute -2 for x in the function f(x):

f(-2)=22(-2)2+5(-2)+2f(-2)=42-52+2f(-2)=0

As f(-2)=0, the given polynomial g(x) is a factor of f(x).

Hence, the polynomial g(x)=x+2 is a factor of f(x)=22x2+5x+2


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