Mabel claims that the expression (2 x 2 - x - 15) + (x - 3) (x + 7) is equivalent to 3 (x - 3) (x + k).

For the case where Mabel's claim is true, what must be the value of k?

k=

k = 4

Step-by-step explanation:

In order for the claim to be true, (x-3) must be a factor of each of the terms in the first expression. That is, you must have that expression factor as ...

(x - 3) (2x + 5) + (x - 3) (x + 7)

Factoring out (x - 3), we get ...

= (x - 3) (2x + 5 + x + 7) = (x - 3) (3x + 12)

= 3 (x - 3) (x + 4)

The value of k must be 4.