A trinomial is a polynomial made up of three terms. Factoring trinomials is the inverse of multiplying two binomials

Instead of multiplying two binomials to get a trinomial, you will write the trinomial as a product of two binomials

The general form of a trinomial is ax

Your goal in factoring trinomials is to make ax

When a = 1, the trinomial becomes x

Factor x

x

We are 100 % sure that the first term for each binomial must be x because x * x = x

We also know for sure that ? * ? or the product of the second term for each binomial is equal to 6

-6 is equal to:

6 × 1

-6 × - 1

2 × 3

-2 × -3

The only pair of factors that will add up to 5 is 2 and 3 because 2 + 3 = 56 × 1

-6 × - 1

2 × 3

-2 × -3

Just replace the two question mark by 2 and 3 and you are done

Therefore, x

Notice that (x + 3) * (x + 2) = also equal to (x + 2) * (x + 3) since multiplication is commutative

The final step is to check your answer by multiplying the two binomials

x * x = x

x * 2 = 2x

3 * x = 3x

3 * 2 = 6

Since 2x + 3x = 5x, putting it all together, we get:

x

Factor x

It is almost the same equation as before with the exception that the coefficient of the second term is -5 instead of 5

Follow all steps outlined above. The only difference is that you will be looking for factors of 6 that will add up to -5 instead of 5.

-3 and -2 will do the job

So, x

Factor x

First, notice that x

x

Find factors of -20 that will equal to -1

-20 is equal to

-20 * 1

20 * -1

10 * -2

-10 * 2

4 * -5

-4 * 5

Since 4 + -5 = -1, we have found what we need.
x-20 * 1

20 * -1

10 * -2

-10 * 2

4 * -5

-4 * 5