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Question
Factorise the following:
6y2 + 19y + 15
Sum
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Solution
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)
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