RV-03-001 · Common factor followed by double brackets

Factorise fully $5x^{2} + 30x - 360$ .

Factorising: Common Factor Followed by Double Brackets Booklet p. 4 & p. 5

Method

1) Factor out numerical HCF k first

2) Factorise the monic quadratic inside using a × c and a 2×2 grid

Worked Example (RV-03-001)

① Booklet p. 4 — Factor out numerical HCF

\mathbf{5}

first:

\quad 5(x^2 + 6x - 72)

② Factorise quadratic

(x^2 + 6x - 72)

using 2×2 Grid (Booklet p. 5):

×	$x$	$-6$
$x$	$x^2$	$-6x$
$+12$	$+12x$	$-72$

a \times c = 1 \times (-72) = -72

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

-6 + 12 = +6

✔

\text{Brackets: } \mathbf{(x + 12)(x - 6)}

5(x + 12)(x - 6)