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Factoring Polynomials by Completing the Square

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Perfect Square Trinomials l Examples l x 2 + 6x + 9 l x 2 - 10x + 25 l x 2 + 12x + 36

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

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Perfect Square Trinomials l Create perfect square trinomials. l x 2 + 20x + ___ l x 2 - 4x + ___ l x 2 + 5x + ___ 100 4 25/4

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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

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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.

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

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

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X 2 – 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.

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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 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.

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Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

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Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers.

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