Question

For all integer values of x and constant k, if (x+6)(x+k)=x^2+14x+48, what is the value of k?

Answer 1

8

Explanation:

The product of terms on the left of the equal sign is ...

(x+6)(x+k) = x^2 +(6+k)x +6k

So, you have two clues to the value of k. The coefficient of x must match, and the constant must match.

6+k = 14 ⇒ k = 8

6k = 48 ⇒ k = 8

The value of k is 8.