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Let’s see how this works by looking at several polynomials. We’ll take it step by step, starting with monomials, and then progressing to polynomials with more terms.
A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees. Get in the habit of writing the term with the highest degree first.
Find the degree of the following polynomials.
Find the degree of the following polynomials:
ⓐ ⓑ ⓒ ⓓ ⓔ
ⓐ ⓑ ⓒ ⓓ 3 ⓔ 0
Find the degree of the following polynomials:
ⓐ ⓑ ⓒ ⓓ ⓔ
ⓐ ⓑ ⓒ ⓓ 2 ⓔ 3
You have learned how to simplify expressions by combining like terms. Remember, like terms must have the same variables with the same exponent. Since monomials are terms, adding and subtracting monomials is the same as combining like terms. If the monomials are like terms, we just combine them by adding or subtracting the coefficient.
Remember that like terms must have the same variables with the same exponents.
We can think of adding and subtracting polynomials as just adding and subtracting a series of monomials. Look for the like terms—those with the same variables and the same exponent. The Commutative Property allows us to rearrange the terms to put like terms together.
Find the sum:
| Identify like terms. |
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| Rearrange to get the like terms together. |
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| Combine like terms. |
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Find the difference:
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| Distribute and identify like terms. |
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| Rearrange the terms. |
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| Combine like terms. |
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Subtract: from .
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| Distribute and identify like terms. |
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| Rearrange the terms. |
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| Combine like terms. |
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