factoring (algebra)

• Factoring the greatest common factor (GCF)

  1. Identify the GCF

  2. Divide the first term by the GCF

  3. Divide the second term by the GCF
• Factoring by grouping


  1. Separate into two parts

  2. Take out the GCF for each part

  3. Look for a common term
• Factoring trinomials (leading coefficient is 1)


  1. Find two numbers that multiply to the constant term and add to the middle coefficient

  2. Write as (x + a)(x + b)
• Factoring trinomials (leading coefficient not 1)

  1. Multiply the leading coefficient and constant term

  2. Find two numbers that multiply to the result and add to the middle coefficient

  3. Replace the middle term

  4. Factor by grouping
• Factoring perfect square trinomials

  1. Take the square root of the first and last terms

  2. Multiply the square roots and double it

  3. If it equals the middle coefficient, it's a perfect square trinomial
• Difference of squares can be factored as (a + b)(a - b)
• Factoring a binomial


  1. Take out the GCF

  2. Set each factor equal to 0 to solve for x
• Factoring a trinomial with leading coefficient 1

  1. Find two numbers that multiply to give the constant term and add to give the coefficient of the linear term

  2. Set each factor equal to 0 to solve for x
• To solve equations by factoring:

  1. Factor the expression

  2. Set each factor equal to 0

  3. Solve for x