Question

Which of the following is a factor of $x^2-6x-16$?

• A. x + 8
• B. 8 - x
• C. x - 2
• D. x - 6

Answer 1

The correct option is B

8 - x

The given algebraic equation is $x^2-6x-16$.
We can factorize this using the following identity using,
$(x+a)(x+b)=x^2+(a+b)x+ab$
So, we have to first find the factors of 16.
$8\times 2=4\times 4=16$
We can see that, $8-2=6$.
So, we split the expression as shown
$x^2+2x-8x-16$
$=x(x+2)-8(x+2)$
$=(x+2)(x-8)$
Hence $x-8$ is a factor of the given expression.