How to Factor Trinomials? (+FREE Worksheet!)
Learn how to use FOIL, “Difference of Squares” and “Reverse FOIL” to factor trinomials.
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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”:
\(\color{blue}{x^2+(b+a)x+ab=(x+a)(x+b)}\)
For education statistics and research National Center for Education Statistics.
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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 \(x^2+3x: x(x+3)\), 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 \(x^2-4x: x(x-4)\), 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: \((x+2)(x-4)\)
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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
- \(\color{blue}{(x – 3) (x – 4)}\)
- \(\color{blue}{(x – 2) (x + 7)}\)
- \(\color{blue}{(x + 3) (x – 14)}\)
- \(\color{blue}{(2x + 3) (3x – 4)}\)
- \(\color{blue}{(x – 15) (x – 2)}\)
- \(\color{blue}{(x + 3) (x + 5)}\)
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