adding and subtracting polynomials

1. Adding and Subtracting
Polynomials
Presentation by
E Whitener Using PowerPoint
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2. Let’s take a look at this example of adding polynomials.
(3x2 + 5 – 2x) + (5x + 4x2 – 2)
(3x2 – 2x + 5) + (4x2 + 5x – 2)
3x2 – 2x + 5
4x2 + 5x – 2
7x2 + 3x + 3
1. Re arrange the terms
Exponents in decreasing order.
2. Stack the polynomials.
Be sure you match the like terms, same variable and exponent.
3. Combine like terms
Notice: The variable and exponents DO NOT change

3. (–8x + x2 + 4 ) + (5x – 6 - 3x2)
(x2 – 8x + 4) + (-3x2 + 5x – 6)
x2 – 8x + 4
-3x2 + 5x – 6
-2x2 - 3x – 2
Now another example!
1. Re arrange the terms.
2. Stack the polynomials.
3. Combine like terms.

4. Now we will look at how to subtract polynomials.
To subtract polynomials, you will need to use the
definition of subtraction!
Subtraction is adding the opposite, for example:
becomes
becomes
becomes
becomes
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5. Let’s see how all these pieces fit together.
Stack Polynomials

6. Now let’s look at an example of subtracting polynomials.
(6x2 + 11x – 3) – (3x2 - 5x + 9)
(6x2 + 11x – 3) + (-3x2 + 5x - 9)
6x2 + 11x – 3
-3x2 + 5x - 9
3x2 + 16x - 12
1. Add the opposite of each term .
Change each sign in the 2nd polynomial.
2. Stack the polynomials.
Put like terms together just like for addition.
3. Combine like terms.

7. If you change subtraction to adding the opposite,
then you can combine like terms!
(x2 + 7x – 7) – (3x2 - 5x + 3)
(x2 + 7x – 7) + (-3x2 + 5x -3)
x2 + 7x – 7
-3x2 + 5x -3
-2x2 + 5x -10
1. Add the opposite of each term .
2. Stack the polynomials.
3. Combine like terms.

8. So. . .
now you see that if you know
how to add polynomials, you
know how to subtract
polynomials!
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