Question

Find all solutions by factoring.
4v2 - 25v = 21

Answer 1

(4v + 3) and (v - 7)

Explanation:

First rewrite 4v2 - 25v = 21 as 4v^2 - 25v - 21.

Let's now analyze -25v and -21. We need to identify two integers whose product is 21 and whose sum is -25.

Note that factors of -21 are ±1, ±3, ±7 and ±21. Factors of 4 (the coefficient of v^2) are ±1, ±2 and ±4.

Check out the following trial factors: (4v + 3) and (v - 7). Does this product come out to the given 4v^2 - 25v - 21? Yes. So the desired factors of 4v2 - 25v = 21 are (4v + 3) and (v - 7). Note how (3)(-7) = -21 and how 4(-7) + 3v add up to -25, the coefficient of the v term.