P.3 Factoring
Warmup
Simplify without using a calculator.
Rationalize the Denominator.
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Class Notes
Factoring ­ Writing a polynominal as a product.
Completely factored ­ Each of its factors is prime (i.e., cannot be further factored using integer coefficients).
Common factor
1. (x ­ 2)(2x) + (x ­ 2)(3)
Difference of Two Squares
(u2 ­ v2) = (u + v)(u ­ v)
2. 16x4­81
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Perfect Square Trinomial
u2 + 2uv + v2 = (u + v)2
u2 ­ 2uv + v2 = (u ­ v)2
3. x2 + 10x + 25
4. 9x2 ­ 12x + 4
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Sum or Difference of Two Cubes
u3 + v3 = (u + v) (u2 ­ uv + v2)
Crummy Crummy S OP S
Cr: cube root S:Square of 1st term OP: Opposite Product of the terms S:Square of the 2nd term
u3 ­ v3 = (u ­ v)(u2 + uv + v2)
Examples
5. x3 ­ 27
6. z3 + 125
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Answers to HW Problems
69. 2(x+4)
72. 2x(2x2 ­ 3x + 6)
75. (x ­ 8) (x + 8)
78. 4(1 ­ 3y)(1 + 3y)
81. (x ­ 3)(x + 1)
84. (x + 5)2
87. (2t + 1)2
93. (y + 6)(y2 ­ 6y + 36)
167. A = 4(x ­ 6)(x + 6)
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