How do i factor this?
b. 8x2 + 24x + 10

2(2x + 1)(2x + 5)

Step-by-step explanation:

Given

8x² + 24x + 10 ← factor out 2 from each term

= 2(4x² + 12x + 5)

To factorise the quadratic

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 = 4 × 5 = 20 and sum = + 12

The factors are + 2 and + 10

Use these factors to split the x- term

4x² + 2x + 10x + 5 ( factor the first/second and third/fourth terms )

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

= (2x + 1)(2x + 5), thus

4x² + 12x + 5 = (2x + 1)(2x + 5) and

8x² + 24x + 10 = 2(2x + 1)(2x + 5) ← in factored form