Factor completely 4 а^2 - 8 а - 5

(2a + 1) (2a - 5)

Step-by-step explanation:

Given

4a² - 8a - 5

Consider the factors of the product of the coefficient of the a² term and the constant term which sum to give the coefficient of the a - term

product = 4 * - 5 = - 20 and sum = - 8

The factors are + 2 and - 10

Use these factors to split the a - term

4a² + 2a - 10a - 5 (factor the first/second and third/fourth terms)

= 2a (2a + 1) - 5 (2a + 1) ← factor out (2a + 1) from each term

= (2a + 1) (2a - 5)