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

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 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

27 47( )

4 16x

7 47( )

4 4

7 47

4 4

7 47

4

x

ix

ix

Solving Quadratic Equations by Completing the Square

2

2

2

2

2

1. 2 63 0

2. 8 84 0

3. 5 24 0

4. 7 13 0

5. 3 5 6 0

x x

x x

x x

x x

x x

Try the following examples. Do your work on your paper and then check your answers.

1. 9,7

2.(6, 14)

3. 3,8

7 34.

2

5 475.

6

i

i