Which of the following is a factor of x 2 − 6 x − 16 ? Options: A . &nbsp x + 8 B . &nbsp x − 8 C . &nbsp x − 2 D . &nbsp x − 6

Answer: Option B : B The given algebraic equation is x 2 − 6 x − 16 . We can factorize this using the following identity using, ( x + a ) ( x + b ) = x 2 + ( a + b ) x + a b So, we have to first find the factors of 16. 8 × 2 = 4 × 4 = 16 We can see that, 8 − 2 = 6 . So, we split the expression as shown x 2 + 2 x − 8 x − 16 = x ( x + 2 ) − 8 ( x + 2 ) = ( x + 2 ) ( x − 8 ) Hence x − 8 is a factor of the given expression.

Which of the following is a factor of x2−6x−16?

Question

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

Options:

A .

x + 8

B .

x - 8

C .

x - 2

D .

x - 6

Answer: Option B
:
B

The given algebraic equation is $x^{2} - 6 x - 16$ .
We can factorize this using the following identity using,
$(x + a) (x + b) = x^{2} + (a + b) x + a b$
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
$x^{2} + 2 x - 8 x - 16$
$= x (x + 2) - 8 (x + 2)$
$= (x + 2) (x - 8)$
Hence $x - 8$ is a factor of the given expression.