Factoring Special Cases

1
Section 9.7

• Factoring Special Cases

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Perfect Square Trinomials

• Perfect squares are found by multiplying numbers
  by themselves
• (2)(2 ) 4 (3)(3) 9 (4)(4) 16 (5)(5)
  25 etc

This means that the first term and the last term
of the polynomial are perfect squares
Using the law of exponents, when multiplying like
bases we add the exponents (w)(w) w2, (x)(x)
x2, etc
3
If the first term and last term are perfect
squares, then we can factor them into simple
binomials

• a2 2ab b2 (a b)(a b) (a b)2
• x2 10x 25 (x 5)(x 5) (x 5)2

a2 2ab b2 (a b)(a b) (a b)2 x2
8x 16 (x 4)(x 4) (x 4)2
4

• a2 2ab b2 (a b)(a b) (a b)2
• n2 16n 64 (n 8)(n 8) (n 8)2

c2 12c 36 (c 6)(c 6) (c 6)2
d2 14d 49
(d 7)(d 7) (d 7)2
h2 18h 81
(h 9)(h 9) (h 9)2
g2 8g 16
(g 4)(g 4) (g 4)2
Notice that the coefficient of a is 1
!!!!!!!!!!!!
5

• a2 - 2ab b2 (a - b)(a - b) (a - b)2
• n2 - 10n 25 (n - 5)(n - 5) (n - 5)2

c2 16 64 (c 8)(c - 8) (c - 8)2
d2 24d 144
(d -12)(d - 12) (d - 12)2
h2 -14h 49
(h - 7)(h - 7) (h - 7)2
g2 -6g 9
(g - 3)(g - 3) (g - 3)2
Notice that the coefficient of a is 1
!!!!!!!!!!!!
6
What happens if the coefficient of a is NOT 1
?????

• ax2 2abx b2
• a and b must still be perfect squares to use
  the special rules!!!

9g2 12g 4
(3g)2 12g (2)2
(3g 2)(3g 2) (3g 2)2