How do you factor 12x^2+5x-25??

Question

I am not able to factor this.

Answer 1

Factors of 25 are 1 * 25, 5 * 5

Factors of 12 are 1 * 12, 2 * 6, 3 * 4

Since we're looking for two values that, when the  difference of the products is 5, I'm thinking we need values close together... So I'm going to look at 5*5 and 3 * 4:

(3x + 5)(4x - 5)

Since the constant is -25, i knew that one of my signs was going to be negative.  Since the linear term (5x) was positive, I knew my larger product was going to be positive. 

5 * 4x - 5 * 3x = 20x - 15x = 5x.