Question

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

Answer 1

Answer:

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

Step-by-step 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:

$b=-20+3=-17$

Answer 2

I don’t really know but if you ask a tutor they can help