Factor the following quadratic completely: 8r^2 - 16r - 10 step by step

2(2r + 1)(2r - 5)

Step-by-step explanation:

Given

8r² - 16r - 10 ← factor out 2 from each term

= 2(4r² - 8r - 5)

To factorise the quadratic

Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.

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

The factors are + 2 and - 10

Use these factors to split the r- term

4r² + 2r - 10r - 5 ( factor the first/second and third/fourth terms )

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

= (2r + 1)(2r - 5), so

4r² - 8r - 5 = (2r + 1)(2r - 5) and

8r² - 16r - 10 = 2(2r + 1)(2r - 5) ← in factored form