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Transcript 
9.7 Factor Special Products
Goal • Factor special products – using those patterns we learned!
DIFFERENCE OF TWO SQUARES PATTERN (AKA the sum and difference pattern)
Algebra
a2 – b2 = (a + b)(_____)
Numbers
9x2 – 4 = (3x)2 – 22 = (____)(____)
Example 1 - Factor the polynomial using the difference of two squares pattern.
a. z2 – 81 =
b. 16x 2 – 9 =
c. a2 – 25b2 =
d. 4 – 16n 2 =
=
1. x – 100
2. 49y 2 – 25
3. c 2 – 9d
4. 45 – 80m
5. j 2 + 64
2
2
6. - x 2 + 1
1
Guided Practice Factor the polynomial.
2
Page
e. x2 + 16
Sec 9.7
PERFECT SQUARE TRINOMIAL PATTERN
Algebra a2 + 2ab + b2 = (_________)2
a2 – 2ab+ b2 = (_________)2
Numbers x 2 + 8x +16 =x 2 + 2(x•4) + 42 = (_________)2
x 2 - 6x + 9 =x 2 + 2(x • -3) + (-3)2 = (_________)2
Example 2 - Factor perfect square trinomials
Factor the polynomial.
a. x 2 – 16x + 64 =
b. 4y 2 – 12y + 9 =
c. 9s 2 + 6st + t 2 =
d. –3z 2 + 24z – 48 =
Guided Practice Factor the polynomial.
11. 32x 2 + 32x +16
2
10. -5r 2 – 20r – 20
12. 4x 2 +13x + 9
2
9. 16x 2 – 40xy + 25y
8. 9y 2 – 6y + 1
Page
7. x 2 + 14x + 49
Sec 9.7
Example 3 - Solve a polynomial equation
Solve the equation x² +x + 1 = 0.
4
x2 + x +
1
4
=0
Write original equation
Multiply each side by____
Write left side as a2 + 2ab + b2
Perfect square trinomial pattern
Zero-product property
x =_____
Solve for x
This equation has two ________________________________________, because it has two
____________________________________________.
Example 4 - Solve a vertical motion problem
Falling Object A brick falls off of a building from a height of 144 feet. After how many seconds does
the brick land on the ground?
h = ______
s = ______
v = ______
***NEW***______________________________________________________________
Guided Practice Solve the equation.
Page
3
13. m 2 - 8m + 16 = 0
Sec 9.7
14. w 2 + 16w + 64 = 0
15. t 2 – 121 = 0
Page
4
What If? In Example 4, suppose the brick falls from a height of 225 feet.
After how many seconds does the brick lands on the ground?
4
Sec 9.7
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