Question

The two expressions below are equivalent. Find the values of a and b that make them equivalent.

The two expressions are:
5x^2+bx-12
(5x+a)(x-4)

Answer 1

`a=3\text{ and } b=-17`

Explanation:

We are given that:

`5x^2+bx-12=(5x+a)(x-4)`

First, we can distribute the right-hand side:

`5x(x-4)+a(x-4)`

Distribute:

`=5x^2-20x+ax-4a`

Rewrite:

`=5x^2+(-20+a)x-(4a)`

Since it is equivalent to the above expression, the coefficients of the variables must match. This means that:

`-20+a=b\text{ and } 12=4a`

Solving for a in the second equation gives:

`a=3`

Therefore:

`b=-20+3=-17`