Factoring Polynomials by Completing the Square Perfect Square

Factoring Polynomials by Completing the Square

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

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

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

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

X 2 – 12 x + 4 n n n 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 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.

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

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