Factoring Polynomials by Completing the Square

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

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

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

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

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

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.

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

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

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.

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.

Factoring by Completing the Square

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