Learn how to use FOIL, “Difference of Squares” and “Reverse FOIL” to factor trinomials.

## Related Topics

- How to Multiply Monomials
- How to Multiply and Dividing Monomials
- How to Multiply a Polynomial and a Monomial
- How to Multiply Binomials
- How to Add and Subtract Polynomials

## Step by step guide to Factoring Trinomials

- To factor trinomials sometimes we can use the “
**FOIL**” method (First-Out-In-Last):

\(\color{blue}{(x+a)(x+b)=x^2+(b+a)x+ab}\) - “
**Difference of Squares**”:

\(\color{blue}{ a^2-b^2=(a+b)(a-b)}\)

\( \color{blue}{ a^2+2ab+b^2=(a+b)(a+b)}\)

\( \color{blue}{ a^2-2ab+b^2=(a-b)(a – b)}\) - “
**Reverse FOIL**”:

\(\color{blue}{x^2+(b+a)x+ab=(x+a)(x+b)}\)

### Factoring Trinomials – Example 1:

Factor this trinomial. \(x^2-3x-18=\)

**Solution:**

Break the expression into groups: \((x^2+3x)+(−6x−18)\)

Now factor out \(x\) from \(x^2+3x : x(x+2)\) , and factor out \(−6\) from \(−6x+18: −6(x+3)\)

Then: \(=x(x+3)−6(x+3)\), now factor out like term: \(x+3\)

Then: \((x+3)(x−6)\)

### Factoring Trinomials – Example 2:

Factor this trinomial. \(x^2+x-20=\)

**Solution:**

Break the expression into groups: \((x^2-4x)+(5x-20)\)

Now factor out \(x\) from \(x^2-4x : x(x+3)\) , and factor out \(5\) from \(5x-20: 5(x-4)\)

Then: \(=x(x-4)+5(x-4)\), now factor out like term: \(x-4\)

Then: \((x+5)(x-4)\)

### Factoring Trinomials – Example 3:

Factor this trinomial. \(x^2-2x-8=\)

**Solution:**

Break the expression into groups: \((x^2+2x)+(-4x-8)\)

Now factor out x from \(x^2+2x : x(x+2)\) and factor out \(-4\) from \(-4x-8: -4(x+2)\)

Then: \(=x(x+2)-4(x+2)\) , now factor out like term: \(x+2\)

Then: \((x+2)(x-4)\)

### Factoring Trinomials – Example 4:

Factor this trinomial. \(x^2- 6x+8= \)

**Solution:**

Break the expression into groups: \((x^2-2x)+(-4x+8)\)

Now factor out x from \(x^2-2x : x(x-2)\) , and factor out \(-4\) from \(-4x+8: -4(x-2)\)

Then: \(=x(x-2)-4(x-2) \), now factor out like term: \( x-2\)

Then: \((x-2)(x-4)\)

## Exercises for Factoring Trinomials

### Factor each Trinomial

- \(\color{blue}{x^2 – 7x + 12}\)
- \(\color{blue}{x^2 + 5x – 14}\)
- \(\color{blue}{x^2 – 11x – 42}\)
- \(\color{blue}{6x^2 + x – 12}\)
- \(\color{blue}{x^2 – 17x + 30}\)
- \(\color{blue}{x^2 + 8x + 15}\)

### Download Factoring Trinomials Worksheet

- \(\color{blue}{(x – 3) (x – 4)}\)
- \(\color{blue}{(x – 2) (x + 7)}\)
- \(\color{blue}{(x + 3) (x – 14)}\)
- \(\color{blue}{(2x + 3) (3x – 4)}\)
- \(\color{blue}{(x – 15) (x – 2)}\)
- \(\color{blue}{(x + 3) (x + 5)}\)