Name
LESSON
6-4
Date
Class
Reteach
Factoring Polynomials
Sometimes you can use grouping to factor a third degree polynomial. To factor by grouping
means to group terms with common factors. Then factor the common factors. Continue to
factor until the expression can no longer be factored.
Factor: x 3 4x 2 9x 36.
Start by grouping terms to factor out the greatest possible power of x.
x 2 is a factor of
x 3 and 4x 2.
9 is a factor of 9 and 36.
3
2
x 4x 9x 36
x 3 4x 2 9x 36 x
2
x
4
9 x
x
4
x
4 x 9 x
4 x 3 x 3 2
4 is a common factor.
x 2 9 is the difference of squares.
Recall that a 2 b 2 a b a b . So x 2 9 x 3 x 3 .
Factor each expression.
1. x 3 3x 2 4x 12
2. x 3 6x 2 x 6
x 3 3x 2 4x 12 x 3 6x 2 x 6 x 2 x 6 1 x 6 x 2 x 3 4 x 3 x 3 x 2 4 x 3 x 2 x 2 x 6 x 2 1 x 6 x 1 x 1 3. x3 x2 9x 9
4. x3 2x2 16x 32
x 3 x 2 9x 9 x 3 2x 2 16x 32 x 1 x 2 9 x 1 x 3 x 3 x 2 x 2 16 x 2 x 4 x 4 x 2 x 2 16 x 2 x 2 x 1 9 x 1 Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c06-4_rt.indd 30
30
Holt Algebra 2
12/29/05 8:30:22 PM
Process Black
Name
LESSON
6-4
Date
Class
Reteach
Factoring Polynomials (continued)
Use special rules to factor the sum or difference of two cubes.
Recognizing these common cubes can help you factor the sum or difference of cubes.
3
3
3
3
3
3
1 1, 2 8, 3 27, 4 64, 5 125, and 6 216
3
3
2
2
Rule for the Sum of Two Cubes: a b a b a ab b .
3
Factor: y 64.
y 3 64
Identify the cubes: y 3 and 64 4 3.
y3 43
Write the expression as the sum of two cubes.
(y 4)(y 2 4y 16)
Use the rule to factor.
Using the rule: a y and b 4.
So a 2 y 2, ab 4y, and b 2 16.
Rule for the Difference of Two Cubes: a 3 b 3 (a b)(a 2 ab b 2).
3
Factor: 8x 125.
8x 3 125
2x 3
Identify the cubes: 2x 3 and 125 5 3.
53
Write the expression as the difference of two cubes.
(2x 5)(4x 2 10x 25) Use the rule to factor.
Using the rule: a 2x and b 5.
2
2
2
2
So a 2x 4x , ab 2x 5 10x, and b 25.
Factor each expression.
3
5. 27x 8
6. y 3 216
3x 3 2 3
y3 63
y 6 y 2 6y 36 3x 2 9x 2 6x 4 7. y 27
8. x 1
3
3
y3 33
x3 13
y 3 y 2 3y 9 Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c06-4_rt.indd 31
x 1 x 2 x 1 31
Holt Algebra 2
12/29/05 8:30:23 PM
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Holt Algebra 2