Aim #3: How do we multiply polynomials?
Do Now: Simplify:
a. x(2x + 4)
b.
Multiplying Polynomials
Method 1: Geometric Model
Multiply: (3x + 1)(2x - 5)
2
(2x - 3x + 7)(4x - 3)
Method 2: Distribution
Multiply: (3x + 1)(2x - 5)
2
(2x - 3x + 7)(4x - 3)
HW #2 Solutions: pg 24-25 #3-5, 14-19, 23-25
pg 218 #1-25 odd
3) B
2
14) x
17) 1
4
x
23) 42
x
6
4) B
9 9
15) x y
4
18) x
2
y
3
24) -3x
a
5) C
5
16) 36x
2
3
5
19) a) x (x ) = x
2
2
b) -4 = -16 while (-4) = 16
25) 1
7
w
10
3
3 5
1) 10x
3) -20a
5) -6a b c
4b + 5n
5 7
8
9) -a
11) -48a b
13) 32x
3 2
5t + 2
15 6
17) -3x y
19) -100m
21) 216x y
3 4 8
25) 6a m r
2
7) x
4a
15) -14y
14 19
23) 1 a b
18
Determine the following products:
2
a) (3x + 4x + 2)(2x + 3)
2
2
b) (2x + 10x + 1)(x + x + 1)
3
2
c) (x - 1)(x + 6x - 5)
d) (3x - 5)
2
f) (x + 4)(x - 2y)(3x + 6)
g) (2x + y)
3
e) (5x + 2)(5x - 2)
2
4
h. (3x + x - 1)(x - 2x + 1)
2
i. (2x + 3x + 1)
2
j. Sammy wrote a polynomial using only one variable, x, of degree 3. Myisha wrote a
polynomial in the same variable of degree 5. What can you say about the degree of the
product of Sammy and Myisha's polynomials. Explain.
Sum it up!
• Is the product of two polynomials always going to produce anotherpolynomial?
• Is the square of a polynomial always going to produce anotherpolynomial?
• Which method did you find easier when multiplying polynomials?
(Geometric or Distributive)