Factor Using “COMPLETING THE SQUARE”

Look at these trinomials that are perfect square trinomials.

x2 + 6x + 9 = ( x + 3 ) 2 x2 – 12x + 36 = ( x – 6 ) 2

Notice:

Factoring using “Perfect Square Trinomials” or the “T” Method will give you the square of the binomial outcome.

To complete the square for an expression in the form x2 + bx, you must add to the expression.

Examples: Find n to complete the square.

1. 2. 3.

STEPS TO COMPLETE THE SQUARE:1)

2)

3)

4)

5)

6)

If the leading coefficient is NOT one, divide both sides by the leading coefficient TO MAKE IT A ONE.

Rewrite the equation in the form x2 + bx = c

Write the trinomial as a square

Solve the equation using legal algebra movesRound to the nearest hundredth

The constant is always the square of half of the coefficient of the x-term. Or

2

2

b

2

2

b

Examples:4. 6.

5. 7.