RV-02-001 · Double-bracket factorising: non-monic quadratics

Factorise fully $6x^{2} + 7x - 5$ .

Factorising: Quadratic Expressions a > 1 (Grid Method) Booklet p. 6

Method

1) a × c

2) List factors of ac

3) Select pair which add/subtract to give b

4) Fill in 2×2 grid

5) Take out HCF of top row & factorise outside

6) Brackets

Worked Example (RV-02-001)

Factorising Grid (Booklet p. 6 — Circle HCF

3x

on left):

×	$2x$	$-1$
$3x$	$6x^2$	$-3x$
$+5$	$+10x$	$-5$

a \times c = 6 \times (-5) = -30

c is negative so signs are different (+ and −)...

-3 + 10 = +7

✔

↳ Need to take the HCF out as factor: here

\mathbf{3x}

is the HCF of

6x^2

and

-3x

\text{Brackets: } \mathbf{(3x + 5)(2x - 1)}

(3x + 5)(2x - 1)