Question

Factorise: (7y² – 19y – 6)

Answer 1

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)