# How do you factor the expression x^2+ 2x -3?

Feb 22, 2016

(x + 3 )(x - 1 )

#### Explanation:

To factor , consider the factors of the constant term - 3 which sum to give the coefficient of the x term +2

factors of - 3 are ± (1 , 3 )

The required factors are +3 and - 1 ,as they sum to +2.

$\Rightarrow {x}^{2} + 2 x - 3 = \left(x + 3\right) \left(x - 1\right)$

This may be confirmed by distributing the brackets.

Feb 22, 2016

This is a trinomial of the form $y = a {x}^{2} + b x + c$, which is factored as $\left(x + m\right) \left(x + n\right)$

#### Explanation:

We can find the value of m and n by finding two numbers that multiply to c and that add to b. Two numbers that multiply to -3 and that add to +2 are 3 and -1:

So, when factored, the expression is $\left(x + 3\right) \left(x - 1\right)$

Practice exercises:

1. Find which of the following trinomials are factorable. For those that are, factor them completely.

a) ${x}^{2} + 7 x + 12$

b) ${x}^{2} - 7 x - 12$

c) ${x}^{2} - 7 x + 12$

d) $- {x}^{2} + 7 x - 12$

d) ${x}^{2} + 8 x + 16$

e) ${x}^{2} + 8 x - 16$

f) ${x}^{2} - 8 x + 16$

g) ${x}^{2} + 16$

h) ${x}^{2} - 16$

Good luck!