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Multiplying polynomials
In this PowerPoint presentation you will see two alternative approaches to polynomial multiplication.To see multiplication using a table click here.
To see multiplication “in your head” click here.
Using a table
x² 3x -2
2x²
-x
4
Multiply x² + 3x – 2 by 2x² – x + 4
Using a table
x² 3x -2
2x²
-x
4
Multiply x² by 2x²
Using a table
x² 3x -2
2x² 2x4
-x
4
Multiply x² by 2x²
Using a table
x² 3x -2
2x² 2x4
-x
4
Multiply 3x by 2x²
Using a table
x² 3x -2
2x² 2x4 6x³
-x
4
Multiply 3x by 2x²
Using a table
x² 3x -2
2x² 2x4 6x³
-x
4
Fill in the rest of the table in the same way
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x
4
Fill in the rest of the table in the same way
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³
4
Fill in the rest of the table in the same way
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³ -3x²
4
Fill in the rest of the table in the same way
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³ -3x² 2x
4
Fill in the rest of the table in the same way
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³ -3x² 2x
4 4x²
Fill in the rest of the table in the same way
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³ -3x² 2x
4 4x² 12x
Fill in the rest of the table in the same way
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³ -3x² 2x
4 4x² 12x -8
Fill in the rest of the table in the same way
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³ -3x² 2x
4 4x² 12x -8
Now add up all the terms in the table
First the term in x4
(x² + 3x – 2)(2x² - x + 4) = 2x4
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³ -3x² 2x
4 4x² 12x -8
Now add up all the terms in the table
then the terms in x³
(x² + 3x – 2)(2x² - x + 4) = 2x4 + 5x³
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³ -3x² 2x
4 4x² 12x -8
Now add up all the terms in the table
then the terms in x²
(x² + 3x – 2)(2x² - x + 4) = 2x4 + 5x³
- 3x²
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³ -3x² 2x
4 4x² 12x -8
Now add up all the terms in the table
(x² + 3x – 2)(2x² - x + 4) = 2x4
then the terms in x
+ 5x³
- 3x² + 14x
Using a table
x² 3x -2
2x² 2x4 6x³ -4x²
-x -x³ -3x² 2x
4 4x² 12x -8
Now add up all the terms in the table
(x² + 3x – 2)(2x² - x + 4) = 2x4
and finally the constant term
+ 5x³
- 3x² + 14x- 8
Multiplying polynomials
To see this example of multiplication using a table again click here.
To see multiplication “in your head” click here.
To end this presentation click here.
Multiplying in your head
Multiply x² + 3x – 2 by 2x² – x + 4
(x² + 3x – 2)(2x² – x + 4)
Multiplying in your head
(x² + 3x – 2)(2x² – x + 4)
Start by multiplying the first terms in each bracket to give a term in x4
= 2x4
Multiplying in your head
(x² + 3x – 2)(2x² – x + 4)
Now look for pairs of terms which multiply together to give a term in x³. There are two pairs.
– x³= 2x4
Multiplying in your head
(x² + 3x – 2)(2x² – x + 4)
Now look for pairs of terms which multiply together to give a term in x³. There are two pairs.
– x³ + 6x³
= 2x4
Multiplying in your head
(x² + 3x – 2)(2x² – x + 4)
Now look for pairs of terms which multiply together to give a term in x². There are three pairs.
– x³ + 6x³
+ 4x²= 2x4
Multiplying in your head
(x² + 3x – 2)(2x² – x + 4)
Now look for pairs of terms which multiply together to give a term in x². There are three pairs.
– x³ + 6x³
+ 4x²= 2x4 - 3x²
Multiplying in your head
(x² + 3x – 2)(2x² – x + 4)
Now look for pairs of terms which multiply together to give a term in x². There are three pairs.
– x³ + 6x³
+ 4x²- 3x² - 4x²= 2x4
Multiplying in your head
(x² + 3x – 2)(2x² – x + 4)
Now look for pairs of terms which multiply together to give a term in x. There are two pairs.
= 2x4 – x³ + 6x³
+ 4x²- 3x² - 4x² + 12x
Multiplying in your head
(x² + 3x – 2)(2x² – x + 4)
Now look for pairs of terms which multiply together to give a term in x. There are two pairs.
= 2x4 – x³ + 6x³
+ 4x²- 3x² - 4x² + 12x
+ 2x
Multiplying in your head
(x² + 3x – 2)(2x² – x + 4)
Finally multiply the last two terms in each bracket to give the constant term.
= 2x4 – x³ + 6x³
+ 4x²- 3x² - 4x² + 12x
+ 2x - 8
Multiplying in your head
(x² + 3x – 2)(2x² – x + 4)
Now simplify by collecting like terms.
= 2x4 – x³ + 6x³
+ 4x²- 3x² - 4x² + 12x
+ 2x - 8
= 2x4 + 5x³ - 3x² + 14x - 8
Multiplying polynomials
To see multiplication using a table click here.
To see this example of multiplication “in your head” again click here.
To end this presentation click here.