Question

Which expression has (x – a) as one of its factors?

Answer 1

Answer:

D

Step-by-step explanation:

When an expression is divided by its factor, there are no remainders.

Let's look at the number 6.

6= 1(6)= 2(3)

Thus, the factors of 6 are 1,2,3 and 6.

This is because 6 is divisible by all those numbers to give no remainders.

Let's look at the question again.

D. 2(x-a) is divisible by (x-a) since

$\frac{2(x - a)}{x - a} = 2$

A.

$\frac{ - (x + a) - 2}{x - a}$

This fraction cannot be simplified further

B.

$\frac{ - 2(x + a)}{x - a}$

This fraction cannot be simplified either

C.

$\frac{(x - a) + 2}{x - a} \\ = \frac{x - a}{x - a} + \frac{2}{x - a} \\ = 1 + \frac{2}{x - a}$

There is a remainder of 2 since 2 cannot be divided by (x-a). Thus, (x-a) is not a factor of this fraction.