Question

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

Answer 1

(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.

`rArr x^2 + 2x - 3 = (x + 3 )(x - 1 )`

This may be confirmed by distributing the brackets.

Answer 2

This is a trinomial of the form `y = ax^2 + bx + c`, which is factored as `(x + m)(x + n)`

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 `(x + 3)(x - 1)`

Practice exercises:

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

a) `x^2 + 7x + 12`

b) `x^2 - 7x - 12`

c) `x^2 - 7x + 12`

d) `-x^2 + 7x - 12`

d) `x^2 + 8x + 16`

e) `x^2 + 8x - 16`

f) `x^2 - 8x + 16`

g) `x^2 + 16`

h) `x^2 - 16`

Good luck!