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Unit 13: Factoring

Factoring runs multiplication backward -- you're rebuilding the rectangle whose area is a given expression, one dimension at a time.

6 topics · 20 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Factoring Out the Greatest Common Factor

  1. How it worksHow does finding the greatest common factor of every term let you rewrite an expression as a product?
  2. Worked exampleFind the factored form of 12x3 + 18x2 - 6x after pulling out its greatest common factor.
  3. Common mistakeWhy can't you cancel the x in an expression like 12x3 + 18x2 without factoring it out of every term first?
Your turn1 of 2
Find the factored form of 7x3 + 7x2 - 9x after pulling out its greatest common factor.

Factoring Trinomials with Leading Coefficient 1

  1. How it worksHow does rebuilding a rectangle whose area is x2 + 7x + 12 reveal the two binomial side lengths?
  2. Worked exampleFind the factored form of x2 + 7x + 12.
  3. Worked exampleFind the factored form of x2 - 2x - 15.
  4. Common mistakeWhy doesn't factoring x2 - 5x + 6 mean looking for numbers that add to -5 and multiply to -6?
Your turn1 of 2
Find the factored form of x2 - (7 + -4)x + 7*-4.

Factoring Trinomials with a Leading Coefficient

  1. How it worksHow does splitting the middle term let you factor a trinomial like 2x2 + 7x + 3 by grouping?
  2. Worked exampleFind the factored form of 2x2 + 7x + 3.
  3. Worked exampleFind the factored form of 3x2 - 10x + 8.
  4. Common mistakeWhy can't you factor 2x2 + 7x + 3 by treating it the same way as a trinomial with leading coefficient 1?
Your turn1 of 2
Find the factored form of 3x2 - 3·(5+-2)x + 3·5*-2.

Factoring a Difference of Squares

  1. How it worksHow does recognizing two perfect squares being subtracted let you factor instantly without guessing?
  2. Worked exampleFind the factored form of x2 - 49.
  3. Common mistakeWhy can't a sum of two squares like x2 + 49 be factored the same way a difference of squares can?
Your turn1 of 2
Find the factored form of x2 - 72.

Factoring Perfect Square Trinomials

  1. How it worksHow do you check whether a trinomial's first and last terms are perfect squares that match the middle term?
  2. Worked exampleFind the factored form of x2 + 10x + 25.
  3. Worked exampleFind the factored form of 4x2 - 12x + 9.
Your turn1 of 2
Find the factored form of x2 + 2·7·x + 72.

Factoring by Grouping

  1. How it worksHow does factoring a common term out of each pair set up the same binomial factor in both pairs?
  2. Worked exampleFind the factored form of x3 + 3x2 + 2x + 6 by grouping it into pairs.
  3. Ties togetherHow does factoring by grouping connect back to factoring trinomials with a leading coefficient?
Your turn1 of 2
Find the factored form of x3 + 7x2 + 7x + 7·7 by grouping it into pairs.