1. P.4 Factoring Polynomials
Factor each expression (means factor COMPLETELY)
a. 6x3 – 4x
b. −4x2 + 12x – 16
c. (x – 2)(2x) + (x – 2)(3)
2x(3x2) – 2x(2) =
2x(3x2 – 2)
-4(x2) + (-4)(-3x) + (-4)(4)
-4(x2 − 3x + 4)
(x – 2)(2x + 3)

2. Difference of two squares: Perfect squares trinomial:
Sum or difference of two cubes:
x2 – y2 = (x + y)(x – y)
x2 + 2xy + y2 = (x + y)2
x2 − 2xy + y2 = (x − y)2
x3 + y3 = (x + y)(x2 – xy + y2)
x3 − y3 = (x − y)(x2 + xy + y2)
Ex Factor completely 3 – 12x2
3(1) – 3(4x2) =
3(1 – 4x2) =
3(1 – 2x)(1 + 2x)

3. Ex. 3 Factor completely. a. (x + 4)2 – y2 b. 16x4 – 81
a. x2 – 10x + 25
b x2 + 24x + 9
(x + 4)2 – y2 =
[(x + 4) – y] [(x + 4) + y]
(x + 4 – y)( x y)
(4x2)2 – 92 =
(4x2 – 9) (4x2 + 9)
=[(2x)2 – 32] (4x2 + 9)
=(2x – 3) (2x + 3) (4x2 + 9)
= x2 – 2(5x) + 52 =
(x – 5)2
= (4x)2 + 2(4x)(3) + 32 =
(4x + 3)2

4. Ex. 7 Factor completely. x2 – 7x + 12 +
AND ADDS TO GET 7?
WHAT MULTIPLIES TO GET 12?
(X 3)(X 4) – –
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