5.4 Factor and Solve Polynomial Equations
Sum of Two Cubes:
a3 + b3 = (a + b)(a2 - ab + b2)
Difference of Two Cubes:
a3 - b3 = (a - b)(a2 + ab + b2)
Same
Opposite
Always
Positive
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23 =
33 =
43 =
53 =
63 =
73 =
.
.
.
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1
Examples: Factor the polynomial completely.
1.) x3 - 8
2.) 64y3 + 125
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3.) -3 + 192w3
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2
Example: Factor by grouping.
1.) 25m3 + 125m2 - 4m - 20
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Examples: Factor the polynomial completely.
1.) a4 + 11a2 + 10
2.) 512x6 - 2x2
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3
3.) 12x5 - 18x3 - 210x
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Examples: Find the real-number
solutions of each equation.
-Set equal to zero.
-Factor.
-Set each factor to zero.
1.) 32m3 = 18m
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4
2.) 3x5 + 15x = 18x3
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3.) x6 - 16x4 - 4x2 + 64 = 0
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5