Factoring Quadratics

a

In order to find the greatest common factor, we should factorize both terms and identify which factors are common.

Term	Split up into factors
$5 x$	$5 \cdot x$
$25$	$5 \cdot 5$

When both terms have been broken up into in factors, you see that both contain a 5, and so you can factor this out of the expression. $5 \cdot x + 5 \cdot 5 \Leftrightarrow 5 (x + 5)$

b

Proceed in the same way again and start by splitting the terms into factors.

Term	Split up into factors
$4 a$	$2 \cdot 2 \cdot a$
$4 b$	$2 \cdot 2 \cdot b$

We can find two

2

's in each term. Thus, we can factor out

4 .

2 \cdot 2 \cdot a + 2 \cdot 2 \cdot b

MultiplyMultiply

4 \cdot a + 4 \cdot b

FactorOutFactor out

4

4 (a + b)

c

Split the terms up into factors.

Term	Split up into factors
$81 x$	$3 \cdot 3 \cdot 3 \cdot 3 \cdot x$
$27 y$	$3 \cdot 3 \cdot 3 \cdot y$

Both terms has a factor

27

since

3 \cdot 3 \cdot 3 = 27 .

3 \cdot 3 \cdot 3 \cdot 3 \cdot x - 3 \cdot 3 \cdot 3 \cdot y

MultiplyMultiply

27 \cdot 3 x - 27 \cdot y

FactorOutFactor out

27

27 (3 x - y)

Factoring Quadratics 1.18 - Solution