Which of the binomials below is a factor of this trinomial?

6x^2 - 5x - 25

see explanation

Step-by-step explanation:

Given

6x² - 5x - 25

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

product = 6 * - 25 = - 150 and sum = - 5

The factors are + 10 and - 15

Use these factors to split the x - term

6x² + 10x - 15x - 25 (factor the first/second and third/fourth terms)

= 2x (3x + 5) - 5 (3x + 5) ← factor out (3x + 5)

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

The factors are (3x + 5) and (2x - 5)