Polynomials and Functions aics9e_ppt_5_6.ppt

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
a
2
– b
2
= (a + b) (a – b)
Example:
a.) Factor x
2
– 16.
x
2
– 16 = x
2
– 4
2
= (x + 4)(x – 4)
b.) Factor 25x
2
– 36y
2
.
25x
2
– 36y
2
= (5x)
2
– (6y)
2
=
(5x + 6y)(5x – 6y)

5. 5
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-5
Factor Perfect Square Trinomials
a
2
+ 2ab + b
2
= (a + b)
2
a
2
– 2ab + b
2
= (a – b)
2
Example:
a.) Factor x
2
– 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
x
2
– 8x + 16 = (x – 4)
2

6. 6
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-6
Sum of Two Cubes
a
3
+ b
3
= (a + b) (a
2
– ab + b
2
)
Example:
a.) Factor the sum of cubes x
3
+ 64.

)164)(4(
]4)4()[4(4
))((
2
2233
2233



xxx
xxxx
babababa

7. 7
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-7
Difference of Two Cubes
a
3
– b
3
= (a – b) (a
2
+ ab + b
2
)
Example:
a.) Factor 27x
3
– 8y
6
.
)469)(23(
])2()2)(3()3)[(23(
)2()3(827
4222
22222
32363
yxyxyx
yyxxyx
yxyx




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.
a
3
+ b
3
= (a + b) (a
2
– ab + b
2
)
same sign
The last term in the trinomial will always be positive.
a
3
– b
3
= (a – b) (a
2
+ ab + b
2
)
same sign
opposite sign
always positive
opposite sign
always positive