Answer:
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
