do you remember the theorem

Algebra Level 2

If f ( x ) = 2 x 3 + 6 x 2 − x + 12 f(x)=2x^3+6x^2-x+12 , is x + 2 x+2 a factor of f ( x ) f(x) ?

No. Yes.

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2 solutions

Maximos Stratis
Nov 8, 2017

Assume x + 2 x+2 is a factor of f ( x ) f(x) . Then we have:
f ( x ) = ( x + 2 ) ∗ Q ( x ) f(x)=(x+2)*Q(x)
For x = − 2 x=-2 we get:
f ( − 2 ) = 0 f(-2)=0
So, we have a contradiction since f ( − 2 ) = 22 f(-2)=22 . Therefore x + 2 x+2 is not a factor of x + 2 x+2 .

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Saksham Jain
Nov 8, 2017

USE REMAINDER THEOREM

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