EXAMPLE 1 Complete the square

Find the value of c that makes the expression x2 + 5x + c a perfect square trinomial. Then write the expression as the square of a binomial.

STEP 1Find the value of c. For the expression to be a perfect square trinomial, c needs to be the square of half the coefficient of bx.

Find the square of half the coefficient of bx.2

2 = 254c = 5

EXAMPLE 1 Complete the square

STEP 2Write the expression as a perfect square trinomial. Then write the expression as the square of a binomial.

Substitute 25 for c.

4

x2 + 5x + c = x2 + 5x +254

Square of a binomial52

2+x =

GUIDED PRACTICE for Example 1

Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.

1. x2 + 8x + c ANSWER 16; (x + 4)2

2. x2 12x + c

3. x2 + 3x + c

ANSWER 36; (x 6)2

ANSWER ; (x )294

32