Factoring Trinomials

Factoring Trinomials

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

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

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: \((x+3)(x−6)\)

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

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

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

Factor each Trinomial

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

Download Factoring Trinomials Worksheet

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

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