# Factoring a Quadratic Trinomial

How to factor a quadratic trinomial: examples and their solutions.

## Example 1

Write (*x*)(*x*),

leaving some space after each *x*.

Think of a pair of numbers

whose product is the constant term: +2.

+1 and +2 seems to be good.

So write + 1 and + 2 in each space.

The *x* term found by the FOIL method is,

+2*x* + *x*, +3*x*.

See if this is equal to

the given trinomial's middle term: +3*x*.

It is equal to +3*x*.

So (*x* + 1)(*x* + 2) is the answer.

Finding the right pair of numbers is the triky part.

Here's one of the hints you can use:

Hint #1:

If the middle term and the last term are both (+),

then the pair of numbers are both (+).

## Example 2

Hint #2:

If the middle term is (-) and the last term is (+),

then the pair of numbers are both (-).

Write (*y*)(*y*),

leaving some space after each *y*.

Think of a pair of numbers

whose product is the constant term: +6.

-1 and -6 seems to be good.

So write - 1 and - 6 in each space.

The *y* term found by the FOIL method is,

-6*y* - *y*, -7*y*.

This is not equal to

the given trinomial's middle term: -5*y*.

Then find another pair of numbers

whose product is +6.

-2 and -3 seems to be good.

So write - 2 and - 3 in each space.

The *y* term found by the FOIL method is,

-3*y* - 2*y*, -5*y*.

This is equal to

the given trinomial's middle term: -5*y*.

So (*y* - 2)(*y* - 3) is the answer.

Just like this example,

these problems are solved by trial and error.

## Example 3

Hint #3:

If the last term is (-),

then the pair of numbers are (+) and (-).

Write (*a*)(*a*),

leaving some space after each *a*.

Think of a pair of numbers

whose product is the constant term: -12.

-4 and -3 seems to be good.

So write - 4 and - 3 in each space.

The *a* term found by the FOIL method is,

-4*a* + 3*a*, -*a*.

This is equal to

the given trinomial's middle term: -*a*.

So (*a* - 4)(*a* + 3) is the answer.

## Example 4

Write (2*x*)(*x*),

leaving some space after 2*x* and *x*.

Think of a pair of numbers

whose product is the constant term: +6.

+3 and +2 seems to be good.

So write + 3 and + 2 in each space.

The *x* term found by the FOIL method is,

+4*x* + 3*x*, +7*x*.

This is equal to

the given trinomial's middle term: +7*x*.

So (2*x* + 3)(*x* + 2) is the answer.

## Example 5

Write (*x**y*)(*x**y*),

leaving some space between each *x* and *y*.

Think of a pair of numbers

whose product is the constant term: +24.

+8 and -3 seems to be good.

So write + 8 and - 3 in each space.

The *xy* term found by the FOIL method is,

-3*xy* + 8*xy*, +5*xy*.

This is equal to

the given trinomial's middle term: +5*xy*.

So (*x* + 8*y*)(*x* - 3*y*) is the answer.