1. Multiplying Polynomials
Objective:
Students will multiply polynomials.

2. Algebra Standards:
10.0 Students add, subtract, multiply and divide monomials
and polynomials. Students solve multi-step problems,
including word problems, using these techniques.

3. is a number, a variable, or the product of a number and one or more
Vocabulary
Monomial
is a number, a variable, or the
product of a number and one or more
variables with whole number
exponents. 8
-2x
-3x2y
½x2
Degree of a Monomial
is the sum of the exponents of the variables in
the monomial.
-2x
-3x2y 5
-3x5 1 3 5

4. Vocabulary
Polynomial
is a monomial or a sum of monomials
4x3
-2x + 2
7x2 – 4x + 6
Binomial:
two-term polynomial
x + 2
4x3 + 2x
-2x2 – 5
Trinomial:
three-term polynomial
x2 + 2x – 1
5x5 – 5x + 2
-x4 + 2x2 – 4x

5. Polynomial Degree Identified by Degree Identified by Number of Terms
#1 Identify Polynomials
Polynomial
Degree
Identified
by Degree
Identified by
Number of Terms
a) -3
constant
monomial 1
linear
binomial
b) –x + 1 2
quadratic
binomial
c) x2 + 3
d) 5x3 – 3x2 + x – 8 3
cubic
polynomial

6. a) 4(x +3) = 4x + 12 b) -4a(a +3) = -4a2 – 12a c) 4b(2b2 + 3b – 2) =
#1 Distributive Property
a) 4(x +3) = 4x
+ 12
b) -4a(a +3) =
-4a2
– 12a
c) 4b(2b2 + 3b – 2) =
8b3
+ 12b2
– 8b

7. a) (x + 3) (x – 2) First Outer Inner Last x2 -2x +3x -6 x2 + x – 6
#2 Use FOIL
a) (x + 3) (x – 2)
First
Outer
Inner
Last x2
-2x
+3x -6 x2
+ x
– 6
b) (3x – 2) (x + 2)
First
Outer
Inner
Last
3x2
+6x
-2x -4
3x2
+ 4x
– 4

8. (5x – 4) (3x – 6) First Outer Inner Last 15x2 -30x -12x +24 15x2 – 42x
Check Point:
(5x – 4) (3x – 6)
First
Outer
Inner
Last
15x2
-30x
-12x
+24
15x2
– 42x
+ 24
d) (2x + 3)(x + 10)
First
Outer
Inner
Last
2x2
+20x
+3x
+30
2x2
+ 23x
+ 30

9. (4 – x)(8 – 11x + x2) = 32 – 44x + 4x2 – 8x + 11x2 – x3 = – x3 + 15x2
#3 Distributive Property – more than two terms
(4 – x)(8 – 11x + x2) = 32
– 44x
+ 4x2
– 8x
+ 11x2
– x3 =
– x3
+ 15x2
– 52x
+ 32
b) (x + 2)(x2 – 3x + 5) = x3
– 3x2
+ 5x
+ 2x2
– 6x
+ 10 = x3
– x2
– x
+ 10

10. Assignment
Book Pg. 531
# 3-11, odds ( use FOIL or Box )