Perfect Square Trinomial

Factoring: Perfect Square Trinomials

The first criteria of a Perfect Square Trinomial is that it must have three terms.

Using FOIL we find the product of two binomials.

))(( baba

2a ab ab 2b22 2 baba

Recognizing a Perfect Square Trinomial

25102 xx• First term must be a perfect square.

(x)(x) = x2

• Last term must be a perfect square. (5)(5) = 25

• Middle term must be twice the product of the square root coefficient of the first and last term. (2)(5)(1) = 10

What if it is a Perfect Square Trinomial

• If you have a perfect Square Trinomial it is easy to factor: Take the square root of the first

term. Take the square root of the last term. Use the sign of the middle term, put

in parenthesis and square the result.

25102 xx 2)5( x

25102 xx

Recognizing a Perfect Square Trinomial

1682 mm• First term must be a perfect square.

(m)(m) = m2

• Last term must be a perfect square. (4)(4) = 16

• Middle term must be twice the product of the square root coefficient of the first and last term.

(2)(4)(1) = 8

2)4( m

Recognizing a Perfect Square Trinomial

81182 pp• First term must be a perfect square.

(p)(p) = p2

• Last term must be a perfect square. (9)(9) = 81

• Middle term must be twice the product of the coefficient of the first and last term.

(2)(9)(1) = 18p

2)9( p

Signs must match!

• First term must be a perfect square. (11p)(11p) = 121p2

• Last term must be a perfect square. (10)(10) = 100

• Middle term must be twice the product of the first and last term.(2)(10)(11p) = 220p

100110121 2 pp

Recognizing a Perfect Square Trinomial

Not a Perfect Square

Trinomial!

Perfect Square Trinomial Y/N

1682 rr

42849 2 pp22 364249 tsts

22 44 nmnm 225502 dd

24 Yes r

227 Yes p

No

No

22 Yes nm

HOMEWORK (1/2 CROSSWISE)

1)Factor x2 + 6x + 92)Factor y2 – 16y + 643)Factor m2 – 12m + 364)Factor 4p2 + 4p + 15)Factor 9k2 + 12k + 4

It has the form of

ax2 + bx + c

Example1. x2 + 5x + 62. x2 - 2x + 83. x2 + 8x + 16