Question

Factorise the following:

6y² + 19y + 15

Answer 1

Given: 6y² + 19y + 15

Step-wise calculation:

1. Multiply (a) and (c) where the quadratic is in the form (ay² + by + c): 

a × c = 6 × 15

a × c = 90

2. Find two numbers whose product is 90 and whose sum is 19 the middle coefficient (b): 

9 × 10 = 90

9 + 10 = 19

3. Split the middle term using these two numbers:

6y² + 9y + 10y + 15

4. Factor by grouping:

3y(2y + 3) + 5(2y + 3)

5. Factor out the common binomial:

(2y + 3)(3y + 5)