Mathematics 7

1. 1
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1
Polynomials
and Polynomial
Functions
Chapter 5

2. 2
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-2
5.1 – Addition and Subtraction of Polynomials
5.2 – Multiplication of Polynomials
5.3 – Division of Polynomials and Synthetic
Division
5.4 – Factoring a Monomial from a Polynomial
and Factoring by Grouping
5.5 – Factoring Trinomials
5.6 – Special Factoring Formulas
5.7-A General Review of Factoring
5.8- Polynomial Equations
Chapter Sections

3. 3
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-3
§ 5.6
Special Factoring
Formulas

4. 4
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-4
Difference of Two Squares
a2
– b2
= (a + b) (a – b)
Example:
a.) Factor x2
– 16.
x2
– 16 = x2
– 42
= (x + 4)(x – 4)
b.) Factor 25x2
– 36y2
.
25x2
– 36y2
= (5x)2
– (6y)2
=
(5x + 6y)(5x – 6y)

5. 5
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-5
Factor Perfect Square Trinomials
a2
+ 2ab + b2
= (a + b)2
a2
– 2ab + b2
= (a – b)2
Example:
a.) Factor x2
– 8x + 16.
To determine whether this is a perfect
square trinomial, take twice the product of
x and 4 to see if you obtain 8x.
2(x)(4) = 8x
x2
– 8x + 16 = (x – 4)2

6. 6
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-6
Sum of Two Cubes
a3
+ b3
= (a + b) (a2
– ab + b2
)
Example:
a.) Factor the sum of cubes x3
+ 64.
)
16
4
)(
4
(
]
4
)
4
(
)[
4
(
4
)
)(
(
2
2
2
3
3
2
2
3
3














x
x
x
x
x
x
x
b
ab
a
b
a
b
a

7. 7
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-7
Difference of Two Cubes
a3
– b3
= (a – b) (a2
+ ab + b2
)
Example:
a.) Factor 27x3
– 8y6
.
)
4
6
9
)(
2
3
(
]
)
2
(
)
2
)(
3
(
)
3
)[(
2
3
(
)
2
(
)
3
(
8
27
4
2
2
2
2
2
2
2
2
3
2
3
6
3
y
xy
x
y
x
y
y
x
x
y
x
y
x
y
x












8. 8
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-8
Helpful Hint for Factoring
When factoring the sum or difference of two cubes, the sign
between the terms in the binomial factor will be the same as the
sign between the terms.
The sign of the ab term will be the opposite of the sign between
the terms of the binomial factor.
a3
+ b3
= (a + b) (a2
– ab + b2
)
same sign
The last term in the trinomial will always be positive.
a3
– b3
= (a – b) (a2
+ ab + b2
)
same sign
opposite sign
always positive
opposite sign always positive