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Find the degree of the following polynomials:
ⓐ | |
The exponent of is one. | The degree is 1. |
ⓑ | |
The highest degree of all the terms is 3. | The degree is 3 |
ⓒ | |
The degree of a constant is 0. | The degree is 0. |
ⓓ | |
The highest degree of all the terms is 2. | The degree is 2. |
ⓔ | |
The highest degree of all the terms is 1. | The degree is 1. |
Find the degree of the following polynomials:
Find the degree of the following polynomials:
Working with polynomials is easier when you list the terms in descending order of degrees. When a polynomial is written this way, it is said to be in standard form . Look back at the polynomials in [link] . Notice that they are all written in standard form. Get in the habit of writing the term with the highest degree first.
In The Language of Algebra , you simplified expressions by combining like terms. Adding and subtracting monomials is the same as combining like terms. Like terms must have the same variable with the same exponent. Recall that when combining like terms only the coefficients are combined, never the exponents.
Simplify:
Combine like terms. |
Remember, and are not like terms. The variables are not the same.
Adding and subtracting polynomials can be thought of as just adding and subtracting like terms. Look for like terms—those with the same variables with the same exponent. The Commutative Property allows us to rearrange the terms to put like terms together. It may also be helpful to underline, circle, or box like terms.
Find the sum:
Identify like terms. | |
Rearrange to get the like terms together. | |
Combine like terms. |
Parentheses are grouping symbols. When we add polynomials as we did in [link] , we can rewrite the expression without parentheses and then combine like terms. But when we subtract polynomials, we must be very careful with the signs.
Find the difference:
Distribute and identify like terms. | |
Rearrange the terms. | |
Combine like terms. |
Subtract: from
Distribute and identify like terms. | |
Rearrange the terms. | |
Combine like terms. |
In The Language of Algebra we evaluated expressions. Since polynomials are expressions, we'll follow the same procedures to evaluate polynomials—substitute the given value for the variable into the polynomial, and then simplify.
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