Write this trinomial in factored form 4b^2 + 17b + 15

(b + 3) (4b + 5)

Step-by-step explanation:

Given

4b² + 17b + 15

Consider the factors of the product of the b² term and the constant term which sum to give the coefficient of the b - term.

product = 4 * 15 = 60 and sum = 17

The factors are 12 and 5

Use these factors to split the b - term

4b² + 12b + 5b + 15 (factor the first/second and third/fourth terms)

= 4b (b + 3) + 5 (b + 3) ← factor out (b + 3) from each term

= (b + 3) (4b + 5) ← in factored form