1. Warm Up Factor each expression. 1. 3x – 6y 3(x – 2y) 2. a2 – b2
(a + b)(a – b)
Find each product.
3. (x – 1)(x + 3)
x2 + 2x – 3
4. (a + 1)(a2 + 1)
a3 + a2 + a + 1

2. Objectives
Use the Factor Theorem to determine factors of a polynomial.
Factor the sum and difference of two cubes.

3. You are already familiar with methods for factoring quadratic expressions. You can factor polynomials of higher degrees using many of the same methods you learned in Lesson 5-3.

4. Example 2: Factoring by Grouping
Factor: x3 – x2 – 25x + 25.
(x3 – x2) + (–25x + 25)
Group terms.
Factor common monomials from each group.
x2(x – 1) – 25(x – 1)
Factor out the common binomial (x – 1).
(x – 1)(x2 – 25)
Factor the difference of squares.
(x – 1)(x – 5)(x + 5)

5. Check It Out! Example 2a
Factor: x3 – 2x2 – 9x + 18.
(x3 – 2x2) + (–9x + 18)
Group terms.
Factor common monomials from each group.
x2(x – 2) – 9(x – 2)
Factor out the common binomial (x – 2).
(x – 2)(x2 – 9)
Factor the difference of squares.
(x – 2)(x – 3)(x + 3)

6. Check It Out! Example 2b
Factor: 2x3 + x2 + 8x + 4.
(2x3 + x2) + (8x + 4)
Group terms.
Factor common monomials from each group.
x2(2x + 1) + 4(2x + 1)
Factor out the common binomial (2x + 1).
(2x + 1)(x2 + 4)
(2x + 1)(x2 + 4)

7. Just as there is a special rule for factoring the difference of two squares, there are special rules for factoring the sum or difference of two cubes.

8. Example 3A: Factoring the Sum or Difference of Two Cubes
Factor the expression.
4x x
4x(x3 + 27)
Factor out the GCF, 4x.
4x(x3 + 33)
Rewrite as the sum of cubes.
Use the rule a3 + b3 = (a + b)  (a2 – ab + b2).
4x(x + 3)(x2 – x  )
4x(x + 3)(x2 – 3x + 9)

9. Example 3B: Factoring the Sum or Difference of Two Cubes
Factor the expression.
125d3 – 8
Rewrite as the difference of cubes.
(5d)3 – 23
(5d – 2)[(5d)2 + 5d  ]
Use the rule a3 – b3 = (a – b)  (a2 + ab + b2).
(5d – 2)(25d2 + 10d + 4)

10. Check It Out! Example 3a
Factor the expression.
8 + z6
Rewrite as the difference of cubes.
(2)3 + (z2)3
(2 + z2)[(2)2 – 2  z + (z2)2]
Use the rule a3 + b3 = (a + b)  (a2 – ab + b2).
(2 + z2)(4 – 2z + z4)

11. Check It Out! Example 3b
Factor the expression.
2x5 – 16x2
2x2(x3 – 8)
Factor out the GCF, 2x2.
Rewrite as the difference of cubes.
2x2(x3 – 23)
Use the rule a3 – b3 = (a – b)  (a2 + ab + b2).
2x2(x – 2)(x2 + x  )
2x2(x – 2)(x2 + 2x + 4)

12. Holt Chapter 5 Section 4 Page 431 #2a, 2b Page 433 #4-9, 26-31
Homework!
Holt Chapter 5 Section 4
Page 431 #2a, 2b
Page 433 #4-9, 26-31