Factoring trinomials when a is equal to 1

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 ax² + bx + c. Your goal when factoring trinomials is to make  ax² + bx + c equal to (? + ?) * (? + ?).

Example #1:

Factor x² + 5x + 6

x² + 5x + 6 will look like (x + ?) * (x + ?)

We are 100% sure that the first term for each binomial must be x because x * x = x².

Now, how do we get the second term for each binomial?

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

Finally, we know that x * ? and ? * x must give the second term, which is 5x when added.

The last term of x² + 5x + 6 is 6 and the coefficient of the second term is 5.

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 = 5.

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

Therefore, x² + 5x + 6 = (x + 3) * (x + 2)

Notice that (x + 3) * (x + 2) is 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 = x²

x * 2 = 2x

3 * x = 3x

3 * 2 = 6

Since 2x + 3x = 5x, putting it all together, we get x² + 5x + 6

Example #2:

Factor x² − 5x + 6

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, x² − 5x + 6 = (x + -3) * (x + -2)

Final example

Factor x² − x − 20

First, notice that x² − x − 20 = x² − 1x − 20 because 1*x = x

x² − x − 20 = (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. x² − x − 20 = (x + 4) * (x + -5)

Try this factoring trinomials quiz to see how well you can factor trinomials.

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