Factoring Worksheet With Examples Page 33
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50EXAMPLE
Use Differences of Two Squares
GEOMETRY
The area of the shaded part of the square is
72 square inches. Find the dimensions of the square.
The area of the square less the area of the triangle equals the
Words
area of the shaded region.
Variable
Let x = the side length of the square.
_
1
2
2
Equation
x
-
x
= 72
2
_
1
2
2
x
−
x
= 72
Original equation
2
_
1
2
= 72
x
Combine like terms.
2
_
1
2
x
- 72 = 0
Subtract 72 from each side.
2
2
x
- 144 = 0
Multiply each side by 2 to remove the fraction.
(x - 12)(x + 12) = 0
Factor the difference of squares.
x - 12 = 0
or x + 12 = 0
Zero Product Property
x = 12
x = -12
Solve each equation.
Since length cannot be negative, the only reasonable solution is 12. The
dimensions of the square are 12 inches by 12 inches.
Is this solution reasonable in
the context of the original problem?
_
1
2
5
DRIVING
.
The formula
s
= d approximates a vehicle’s speed s in
24
miles per hour given the length d in feet of skid marks on dry concrete.
If skid marks on dry concrete are 54 feet long, how fast was the car
traveling when the brakes were applied?
Factor each polynomial, if possible. If the polynomial cannot be factored,
Examples 1–3
(pp. 448–449)
write prime.
2
2
1. n
- 81
2. 4 - 9 a
5
3
4
4
3. 2 x
4. 32 x
- 98 x
- 2 y
2
3
2
5. 4 t
- 27
6. x
- 3 x
- 9x + 27
Solve each equation by factoring. Check the solutions.
Example 4
_
1
2
2
3
(p. 449)
7. 4 y
8. x
9. 121a = 49 a
= 25
-
= 0
36
10.
GEOMETRY
A corner is cut off a 2-inch by 2-inch square
Example 5
(p. 450)
piece of paper as shown. What value of x will result in
_
7
an area that is
the area of the original square?
9
450
Chapter 8 Factoring
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