Download Polynomial Multiplication

Polynomial
Multiplication
By Bryan Neilson
Multiplying simple monomial
 The
idea is to multiply the numbers
and add our exponets
 An example would be (3x2)7x4
 3*7=21
coefficient on new term
 2+4 = 6
power on new term
 Our new term then is 21x6
Do the following Examples
 (2x4)6x3
 (-5x2)10x
 (7x5)(-4x6)
 (-8x)(3x2)
 When
you are done compare your
answers with those of your neighbors
 Teacher walks around room to help
Distributing terms
 2x(3x2
– 6x + 4)
 What we are doing is multiplying
each of the terms inside by 2x in
turn and remove the parenthesis
3
2 +8x
=6x
-12x
 2x(3x2 – 6x + 4)
Distributing a negative
 actively
think about the sign of
answer before you write it down.
 -3x2(2x2
 The
– 4x + 3) = -6x4 +12x3 -9x2
most important thing to notice is
that all the signs change from what
they were.
Try the 2 examples on your own
 2x(4x2
– 6x + 9)
 -3x2(6x3 – 4x2 + 3)
 Once you finish share your results
with your neighbor
 Go
around helping your students if
they have questions
Indian Multiplication
 The
ancient Indians had a method of
multiplication that is different from
our own.
 It was called the Gelosia method
 We will examine the properties of
this system and see if we can’t
modify it to use in algebra
Gelosia Method
In Multiplying 987
X 961
 They placed them
around a table like
this

9
8
7
9
6
1
Mult Col # by
Row # place
answer in the
box
 The number
above the line
represents the
tens position
 Below the ones

9
8
5
0
8
1
4
9
7
4
0
7
6
2
8
4
0
8
3
2
7
9
6
1
Now add #’s along diagonals
Ten’s place of sum
Is a carry
8
8+1=9
5
4
7
7
9
6
2
3
4
4
The answer
is
4
8
948,507
0
0
2
0
9
8
0+4+4+2+6+2=18
8
1
9
5+1+7+1=14
9
8
5
0
9+0+8+4+3+1=25
8+2=10
7
7
6
1
Your goal
 Try
to use the Gelosia Method to
multiply the polynomials
 (2x2 - 3x + 4)(5x - 3)
 Give your students about 5-7
minutes to attempt. Go around the
room to help and check their work.
2x2
-3x
10x3
-6x2
-15x2
9x
+4
20x
5x
-12
-3
One of the beauty of the system is that like terms often wind
3
2
Up along the diagonal making them easy to add
10x
- 21x + 29x - 12
Larger polynomial multiplacation
 Another
interesting property is that it
is probably the best method to use
when multiplying really large
polynomials
 Let’s try to use the Gelosias method
to multiply
2 – 2x + 4)(6x2 – 7x +2)
 (3x
 Give the students some time to try it
on their own
=18x4 – 33x3 + 44x2 -32x +8
3x2
– 2x
+4
6x2
18x4
-12x3
24x2
-21x3
14x2
-28x
– 7x
6x2
-4x
8
+2
Now add along diagnols
Let’s play battleship
 Go
back to the website Quia.com and
complete the polynomial quiz.
 If you have time you can play
polynomial battleship.