Factoring Quadratics

We will start by factoring the left-hand side, and then we will solve the equation.

Consider the left-hand side of the equation.

x^{2} + 3 x + 2

1,

to factor this expression we will find two numbers whose sum is

3

and whose product is

2 .

1 + 2 = 3 and 1 \cdot 2 = 2

As we see above, the sum of

1

and

2

is

3,

and their product is

2 .

Therefore, we will rewrite

3 x

as

x + 2 x .

x^{2} + 3 x + 2 = 0

WriteSumWrite as a sum

x^{2} + x + 2 x + 2 = 0

Factor out

x & 2

FactorOutFactor out

x

x (x + 1) + 2 x + 2 = 0

FactorOutFactor out

2

x (x + 1) + 2 (x + 1) = 0

FactorOutFactor out

(x + 1)

(x + 1) (x + 2) = 0

To solve this equation, we will apply the Zero Product Property.

(x + 1) (x + 2) = 0

ZeroProdPropUse the Zero Product Property

x + 1 = 0 x + 2 = 0 (I) (II)

(I):

LHS - 1 = RHS - 1

x = - 1 x + 2 = 0

(II):

LHS - 2 = RHS - 2

x = - 1 x = - 2

Factoring Quadratics 1.8 - Solution