Question

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=

Answer 1

k = 4

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.