Answer: A trinomial is a polynomial with 3 terms.. This page will focus on quadratic trinomials. The degree of a quadratic trinomial must be '2'. In other words, there must be an exponent of '2' and that exponent must be the greatest exponent.

Examples of Quadratic Trinomials:

3x² + 2x + 1

7x² + 4x + 4

5x² + 6x + 9

Non-Examples of Quadratic Trinomials:

3x^{3} + 2x + 1

this is not a quadratic trinomial because there is an exponent that is greater than 2

2x + 4

this is not a quadratic trinomial because there is not exponent of 2. In fact, this is not even a trinomial because there are 2 terms

5x^{3} + 6x^{2} + 9

this is not a quadratic trinomial because there is an exponent that is greater than 2

Note: For the rest of this page, 'factoring trinomials' will refer to factoring 'quadratic trinomials' . (The only difference being that a quadratic trinomial has a degree of 2.)

Video Tutorial on Factoring Trinomials

Formula For Factoring Trinomials (when a =1)

It's always easaier to understand a new concept by looking at a specific example so you might want to do that first. This formula works when 'a' is 1. In other words, we will use this approach whenever the coefficient in from of x^{2} is 1.

1) identify a,b, and c in the trinomial ax^{2} + bx+c

2) write down all factor pairs of c

3) identify which factor pair from the previous step sums up to b

1) identify a,b, and c in the trinomial ax^{2} + bx+c

a=
1
b=
5
c=
4

2) write down all factor pairs of 4

(Note: since 5 is positive we only need to think about pairs that are either both positive or both negative. Remember a negative times a negative is a positve. As the chart on the right shows you -2*-2 is positive 4...so we do have to consider these two negative factors. This is probabily easier to understand if you watch our video lesson factoring trinonmials)

3) identify which factor pair from the previous step sums up to c

5) If you'd like, you can check your work by multiplying the two binomials and verify that you get the original trinomial

(x +4)(x+1) = x^{2} + 5x + 4

Practice Problems

Problem 1)
Factor the following trinomial:
x^{2}+4x +3

Steps 1 and 2

1) identify a,b, and c in the trinomial
ax^{2} + bx+c

a=
1
b=
4
c=
3

2) write down all factor pairs of 3

Rest of Steps

3) identify which factor pair from the previous step sums up to 4

(Note: since 4 is positive we only need to think about pairs that are either both positive or both negative. Remember a negative times a negative is a positve)

5) If you'd like, you can check your work by multiplying the two binomials and verify that you get the original trinomial

(x +3)(x+1) = x^{2} + 4x + 3

Problem 2)
Factor the trinomial below

x^{2}+5x +6

Steps 1 and 2

1) identify a,b, and c in the trinomial
ax^{2} + bx+c

a=
1
b=
5
c=
6

2) write down all factor pairs of 6

(Note: since 6 is positive we only need to think about pairs that are either both positive or both negative. Remember a negative times a negative is a positve)

Rest of Steps

3) identify which factor pair from the previous step sums up to 5

(Note: since 5 is positive we only need to think about pairs that are either both positive or both negative. Remember a negative times a negative is a positve)

5) If you'd like, you can check your work by multiplying the two binomials and verify that you get the original trinomial

(x +2)(x+3) = x^{2} + 5x + 6

Problem 3)
Factor the trinomial below

x^{2} - 2x -3

Steps 1 and 2

1) identify a,b, and c in the trinomial
ax^{2} + bx+c

a=
1
b= -2
c=
-3

2) write down all factor pairs of -3

(yes, the negative sign matters!)

Rest of Steps

3) identify which factor pair from the previous step sums up to -2

(Note: since c is negative we only need to think about pairs that have 1 negative factor and 1 positve factor. Remember a negative times a positve is a negative)

5) If you'd like, you can check your work by multiplying the two binomials and verify that you get the original trinomial

(x +2)(x- 3) = x^{2 }- 2x -3

Problem 4)
Factor the trinomial below

x^{2 }-5x +6

Steps 1 and 2

1) identify a,b, and c in the trinomial
ax^{2} + bx+c

a=
1
b= -5
c=
6

2) write down the factor pairs of 6

(Note: since 6 is positive we only need to think about pairs that are either both positive or both negative. Remember a negative times a negative is a positve)

Rest of Steps

3) identify which factor pair from the previous step sums up to -5

(Note: since c is negative we only need to think about pairs that have 1 negative factor and 1 positve factor. Remember a negative times a positve is a negative)

5) If you'd like, you can check your work by multiplying the two binomials and verify that you get the original trinomial

(x -2)(x- 3) = x^{2 }-5x +6

Problem 5)
Factor the trinomial below

x^{2 }-2x -15

Steps 1 and 2

1) identify a,b, and c in the trinomial
ax^{2} + bx+c

a=
1
b= -5
c=
6

2) write down the factor pairs of -15

(Note: since c is negative we only need to think about pairs that have 1 negative factor and 1 positve factor. Remember a negative times a positve is a negative)

Rest of Steps

3) identify which factor pair from the previous step sums up to -2