Module 18.2 Multiplying Polynomial Expressions · 1/12/2017 · Module 18.2 Multiplying Polynomial...
Transcript of Module 18.2 Multiplying Polynomial Expressions · 1/12/2017 · Module 18.2 Multiplying Polynomial...
Module 18.2
Multiplying Polynomial Expressions
P. 855
How can you multiply binomials and polynomials?
There are 4 methods; most often you’ll use #1 and #2.
FOIL
FirstOuterInnerLast
P. 857
METHOD #1 of 4
We begin by multiplying two binomials together.
F -->O -->I -->L -->
FOIL
P. 857
P. 857
FOIL
(x – 2) (x – 6) = 𝑥2 – 6x – 2x + 12
= 𝑥2 – 8x + 12 Often – but not always.
(3x + 2) (2x – 3)
P. 856
P. 857
Note
(2x + 1) (x – 3) = 2𝑥2 –5x – 3
METHOD #2 of 4
(2x + 1) (x – 3)
= 2𝑥2 + 1x – 6x – 3
= 2𝑥2 –5x – 3
Create a table.
Note:It doesn’t matter which expression is horizontal or vertical.
Your Turn
4x –7
2x
+3
(4x – 7) (2x + 3)
METHOD #3 of 4
2 6
3 2
5 2
7 8
8 3 2
Vertical format, like multiplying multi-digit whole numbers.
Your Turn
2x – 2
3x + 3
P. 856METHOD #4 of 4
(x – 2) (x – 6) = x(x – 6) –2(x – 6)
= 𝑥2 – 6x – 2x + 12
= 𝑥2 – 8x + 12
Another Example
METHOD #1 of 4
The FOIL Method
Now we multiply a binomial and a trinomial.
Create a table.
Multiplying a binomial and a trinomial
Note:It doesn’t matter which expression is horizontal or vertical. Just be sure there are enough boxes!
METHOD #2 of 4 – USE THIS ONE
We Do
(𝑥4 + 𝑥2 + 1) (x – 4)
METHOD #3 of 4
Vertical format, like multiplying multi-digit whole numbers.
Multiplying a binomial and a trinomial
METHOD #4 of 4 P. 858
P. 859
Use FOIL or any other method you prefer
x + 4
x + 1 A = (x + 4) (x + 1)
Use FOIL or any other method you prefer
P. 859
30
Orik 20 A = (20)(30) = 600
30 – x
Laura 20 - x A = (20 – x)(30 – x)
P. 860
x
x x
x
15
20
(Write a polynomial.)
P. 860