Factor this polynomial expression.

10x2 - 7x-12

(2x - 3) (5x + 4)

Step-by-step explanation:

Given

10x² - 7x - 12

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x - term

product = 10 * - 12 = - 120 and sum = - 7

The factors are - 15 and + 8

Use these factors to split the x - term

10x² - 15x + 8x - 12 (factor the first/second and third/fourth terms)

= 5x (2x - 3) + 4 (2x - 3) ← factor out (2x - 3) from each term

= (2x - 3) (5x + 4)