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Question
Factorise: (7y2 – 19y – 6)
Solution
7y2 – 19y – 6 is of the form ax2 + bx + c where a = 7, b = – 19, c = – 6
| Product = – 42 | Sum = – 19 |
| 1 × – 42 = – 42 | 1 + (– 42) = – 41 |
| 2 × – 21 = – 42 | 2 + (– 21) = – 19 |
The product a × c = 7 × – 6 = – 42
sum b = – 19
The middle term – 19 y can be written as – 21y + 2y
7y2 – 19y – 6 = 7y2 – 21y + 2y – 6
= 7y(y – 3) + 2(y – 3)
= (y – 3)(7y + 2)
7y2 – 19y – 6 = (y – 3)(7y + 2)
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