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Master Factoring Polynomials by Completing the Square Techniques

Learn and practice completing the square method for factoring polynomials. Understand perfect square trinomials with examples.

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Master Factoring Polynomials by Completing the Square Techniques

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  1. Factoring Polynomials by Completing the Square

  2. Perfect Square Trinomials • Examples • x2 + 6x + 9 • x2 - 10x + 25 • x2 + 12x + 36

  3. Creating a Perfect Square Trinomial • In the following perfect square trinomial, the constant term is missing. X2 + 14x + ____ • Find the constant term by squaring half the coefficient of the linear term. • (14/2)2 X2 + 14x + 49

  4. Perfect Square Trinomials • Create perfect square trinomials. • x2 + 20x + ___ • x2 - 4x + ___ • x2 + 5x + ___ 100 4 25/4

  5. Factoring Quadratics by Completing the Square Factor by completing the square: Step 1: First take the coefficient of the linear term, divide it by 2, and then square it. This gives 16 - (8/2)2

  6. What if a is NOT 1 • 3x2 + 6x + c • 2x2 + 5x + c

  7. Factoring by Completing the Square Step 2: Add and subtract 16 just after the linear term. Therefore, you did not change the value of the expression.

  8. Factoring by Completing the Square Step 3: Use brackets to group the first three terms – This is your perfect square trinomial.

  9. Factoring by Completing the Square Step 3: Factor the perfect square trinomial and simplify the rest. (x + 4)2 + 4

  10. X2 – 12x + 4 • Step 1: First take the coefficient of the linear term, divide it by 2, and then square it. • Step 2: Add and subtract 16 just after the linear term. Therefore, you did not change the value of the expression. • Step 3: Use brackets to group the first three terms – This is your perfect square trinomial.

  11. Factor by Completing the Square Step 1: First take the coefficient of the linear term, divide it by 2, and then square it. Step 2: Add and subtract this value. Step 3: Use brackets to group the first three terms – This is your perfect square trinomial.

  12. Factoring by Completing the Square

  13. Factoring by Completing the Square Try the following examples. Do your work on your paper.

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