1. Factoring and Solving Polynomial Equations Section 6.4

2. Special Factoring Patterns
Sum of two cubes
a3 + b3 = (a + b) (a2 − ab + b2)
x = (x + 2) (x2 − 2x + 4)
Difference of two cubes
a3 − b3 = (a − b) (a2 + ab + b2)
8x3 − 1 = (2x − 1) (4x2 + 2x + 1)

3. Factoring the Sum of Difference of Cubes
Factor each polynomial
x3+ 27
16u5 − 250u2

4. Factoring by Grouping Factor the polynomial x3 − 2x2 − 9x + 18
Group the factors x3 − 2x2 − 9x + 18
Take GFC of each x2(x − 2) −9(x − 2)
Reverse distributive (x − 2)(x2 −9)
Factor More??? (x − 2)(x −3)(x + 3)
Factor More??? No—Done!!!

5. Factoring Polynomials in Quadratic Form
Factor each polynomial
81x4 − 16
4x6 − 20x4 + 24x2
=(9x2)2 −42
=(9x2 +4)(9x2 −4)
=(9x2 +4)(3x +2)(3x− 2)
=4x2(x4−5x2 +6)
=4x2(x2−2)(x2−3)

6. Solving a Polynomial Equation
Solve 2x5 + 24x = 14x3
2x5 −14x3 + 24x = 0
2x(x4 −7x2 +12) = 0
2x(x2 −3)(x2 −4) = 0
2x(x2 −3)(x −2)(x + 2) = 0
2x = 0, x2 −3 = 0, x − 2 = 0, x + 2 = 0
x = 0, x = +√3, x = − √3, x = 2, x = −2

7. In 1980 archeologists at the ruins of Caesara discovered a huge hydraulic concrete block with a volume of 330 cubic yards. The block’s dimensions are x yards high by 13x −15 yards wide. What is the height?
Volume =
Height =
Length=
Width=
330 x
13x −11
13x − 15
330 = x(13x −11)(13x −15)
0 = 169x3 −338x x −330
0 = 169x2(x −2) + 165(x − 2)
0 + (169x2 +165)(x − 2)
x = 2 only real solution. So,
13x −15 = 11, 13x − 11 = 15

8. Assignment 6.4
Page 348, even