Factor Trinomials with Two Variables

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Factoring Trinomials
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The following diagram shows how to factor trinomials with two variables. This method only works when the leading coefficient is one. Scroll down the page for examples and solutions for other methods.

 

• Factor Trinomials Worksheets

  Printable
  Factoring Trinomials (a = 1)
  Factoring Trinomials (a > 1)
  Factor Perfect Square Trinomials
  

  Factoring Quadratics (a = 1)
  Factoring Quadratics (a > 1)
  Factor Difference of Squares
  Factor Perfect Square Quadratics
  

  Online
  Factor Binomials by Difference of Squares
  Factor Perfect Square Trinomials
  
  Factor Trinomials or Quadratic Equations
  Factor Different Types of Trinomials 1
  Factor Different Types of Trinomials 2
  
  Solve Trinomials using Quadratic Formula
  Find Discriminants of Quadratic Polynomials

How to factor Trinomials with two variables?
Sometimes a trinomial may consists of two variables. We can factor the trinomial in a similar way as if it has only one variable. We can use the trial and error method (reverse FOIL method), the grouping method or the AC method.

Example:
Factor the following trinomials:
a) e² − 6ef + 9f²
b) 2x² + 7xy − 15y²

Solution:
a) e² − 6ef + 9f² = (e − 3f)²
b) 2x² + 7xy − 15y² = (2x − 3y)(x + 5y)

Factoring trinomials with two variables
Step 1: Find the Product, Sum and the two numbers that “work”
Product = (First number) × (Last number)
Sum = (Middle Number)
Find two numbers that when multiplied gives the Product and when added gives the Sum.
Step 2: Split the middle term.
Step 3: Group in twos and remove the GCF of each group.
Step 4: Write in factored form.

How to factor trinomials with two variables and a = 1?
Some strategies to factor trinomials that have a = 1

Examples:

1. a² - 9ab + 14b²
2. m² - mn - 30n²

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How to factor trinomial with two variables and a > 1?

Example:
18m² - 9mn - 2n²

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Factor trinomial containing two variables
Example:
v² + 5vf - 24f²

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How to factor trinomial with two variables using gcf then grouping?
Example:
6m⁶n + 11m⁵n² + 3m⁴n³

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How to factor a trinomial with two variables using the AC Method?
Example:
30x³y - 25x²y² - 30xy³

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How to Factor Trinomials with Two Variables using the reverse FOIL or trial and error method?
Examples:

1. 12x² - 5xy - 2y²
2. 6x² - 17xy + 10y²

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Example:

1. 2c² + 13cd + 6d²
2. 5x² - 6xy + 1

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