8.2 MULTIPLYING and FACTORING
POLYNOMIALS:
Distributive Property: for any real
numbers a, b, and c :
a(b+c) = (b+c)a = ab + ac.
Greatest Common Factor (GCF): The
number, variable and/or term that each
monomial or polynomial have in common.
GOAL:
MULTIPLYING POLYNOMIALS:
When multiplying polynomials we must keep
in mind the laws of exponents from chapter 7
and the distributive property.
Ex:
What is the simplest for of:
2
–2x
3
2
(7x +5x
– 12)
MULTIPLYING POLYNOMIALS:
Use the distributive property and exponent
rules:
–2x2 (7x3+5x2 – 12)
(–2)(7)x3x2+(–2)(5)x2x2 – (–2)(12) x2
5
–14x
4
–10x
+
2
24x
REAL-WORLD (x): We multiply
polynomials using distributive property
and exponential rules:
Ex: A rectangular wooden frame has side
lengths of 5x and 7x+1.
The rectangular opening for a picture has side
lengths of 3x and 5x. What is the area of the
wooden part of the frame?
SOLUTION:
A rectangular wooden frame :
5x
Area = b.h
7x+1
Area = (7x+1)(5x)
Area of outside =
2
35x
+ 5x
SOLUTION:
The rectangular opening for a picture
has side
Area = b.h
3x
Area = (5x)(3x)
5x
2
Area = 15x
SOLUTION:
What is the area of the wooden part
of the frame?
5x
3x
5x
7x+1
Area of outside: 35x2 + 5x
2
Area of inside : - 15x
Area of wood part:  20x2 + 5x
FINDING THE GCF: Remember that the
Greatest Common Factor (GCF) is what
they have in common:
Ex:
What is the GCF of :
1) 5X3, 25x2 and 45x?
6
4
2
2) 9x +15x +12x
3) p(p + 2) – 5(p + 2)
FINDING THE GCF: Remember that the
Greatest Common Factor (GCF) is what
they have in common:
1) 5x3, 25x2 and 45x?
5x3  5∙x∙x∙x
25x2  5∙5∙x∙x
45x  3∙3∙5∙x
In common:
5x
The GCF is 5x.
FINDING THE GCF: Remember that the
Greatest Common Factor (GCF) is what
they have in common:
1) 9x6+15x4+12x2
9x6  3∙ 3∙x∙x∙x∙x∙x∙x In common:
15x4  3∙5∙x∙x∙x∙x
3xx = 3x2
2
12x  3∙4∙x∙x
The Factored form is: 3x2(3x4+5x2+4)
FINDING THE GCF: Remember that the
Greatest Common Factor (GCF) is what
they have in common:
3) p(p + 2) – 5(p + 2)
p(p + 2)  p∙(p + 2)
– 5(p + 2)  – 5∙(p + 2)
In common
(p + 2)
The Factored form is: (p + 2)(p– 5)
VIDEOS:
Polynomials
Multiplying
Multiplying:
https://www.khanacademy.org/math/trigonometry/polyn
omial_and_rational/polynomial_tutorial/v/multiplyingpolynomials
VIDEOS:
Greatest Common Factor
https://www.khanacademy.org/math/algebra/polyno
mials/multiplying_polynomials/v/monomial-greatestcommon-factor
https://www.khanacademy.org/math/algebra/polynomials/
multiplying_polynomials/v/factoring-and-the-distributiveproperty-2
CLASSWORK:
Page 477-478:
Problems: As many as
needed to master
the concept