1. Warm Up #10 Multiply the polynomial. 1. (x + 2)(x + 3)(x + 1)
ANSWER
(x2 + 5x + 6)(x + 1)
2. (2x – 1)(2x + 1)
ANSWER
4x2 – 1
3. (x – 7)2
ANSWER
x2 – 14x + 49

2. Check HW 5.3

4. Find a common monomial factor
EXAMPLE 1
Find a common monomial factor
Factor the polynomial completely.
a. x3 + 2x2 – 15x
= x(x2 + 2x – 15)
Factor common
monomial.
= x(x + 5)(x – 3)
Factor trinomial.
b. 2y5 – 18y3
= 2y3(y2 – 9)
Factor common
monomial.
= 2y3(y + 3)(y – 3)
Difference of two
squares
c. 4z4 – 16z3 + 16z2
= 4z2(z2 – 4z + 4)
Factor common
monomial.
= 4z2(z – 2)2
Perfect square trinomial

5. Sum and Difference of Cubes:

6. Write each monomial as a cube and apply either of the rules.
Rewrite as cubes
Apply the rule for sum of cubes:

7. Rewrite as cubes
Apply the rule for difference of cubes:

8. GUIDED PRACTICE
for Examples 1 and 2
Factor the polynomial completely.
y5 – 75y3
x3 – 7x2 + 10x

9. 2b2(2b + 7)(4b2 –14b + 49) GUIDED PRACTICE for Examples 1 and 2
Factor the polynomial completely.
b b2
2b2(2b + 7)(4b2 –14b + 49)

10. (w – 3)(w2 + 3w + 9) GUIDED PRACTICE for Examples 1 and 2
Factor the polynomial completely.
4. w3 – 27
(w – 3)(w2 + 3w + 9)

11. Factor by Grouping EXAMPLE 3
Factor the polynomial x3 – 3x2 – 16x + 48 completely.
x3 – 3x2 – 16x + 48
= x2(x – 3) – 16(x – 3)
Factor by grouping.
= (x2 – 16)(x – 3)
Distributive property
= (x + 4)(x – 4)(x – 3)
Difference of two
squares

12. Factor polynomials in quadratic form
EXAMPLE 4
Factor polynomials in quadratic form
Factor completely: (a) 16x4 – 81 and (b) 2p8 + 10p5 + 12p2.
a x4 – 81
= (4x2)2 – 92
Write as difference
of two squares.
= (4x2 + 9)(4x2 – 9)
Difference of two
squares
= (4x2 + 9)(2x + 3)(2x – 3)
Difference of two
squares
Factor common
monomial.
b. 2p8 + 10p5 + 12p2
= 2p2(p6 + 5p3 + 6)
Factor trinomial in
quadratic form.
= 2p2(p3 + 3)(p3 + 2)

13. GUIDED PRACTICE
for Examples 3 and 4
Factor the polynomial completely.
x3 + 7x2 – 9x – 63
ANSWER
(x + 3)(x – 3)(x + 7)

14. GUIDED PRACTICE
for Examples 3 and 4
Factor the polynomial completely.
g4 – 625
(4g2 + 25)(2g + 5)(2g – 5)
ANSWER

15. GUIDED PRACTICE
for Examples 3 and 4
Factor the polynomial completely.
t6 – 20t4 + 24t2
4t2(t2 – 3)(t2 – 2 )
ANSWER

16. Class/Homework Assignment Workbook 5.4 (multiples of 3)