Explore: Polynomials Solutions
- A polynomial expression is a group of one or more terms that follow these rules:
- The variables must have exponents that are whole numbers, and:
- The variables cannot have negative exponents.
- The variables cannot have fractional exponents.
- The variables cannot be in the denominator .
- The variables must have no radical or absolute value symbols.
- The variables must have exponents that are whole numbers, and:
Example 1
Determine if the expression is a polynomial. Explain.
- Yes, this is a polynomial because all the variables have exponents that are whole numbers.
- No, this is NOT a polynomial because the first term has a negative exponent and the second term has a variable in the denominator.
- No, this is NOT a polynomial because the first term has a variable under a radical symbol .
Polynomials have whole number exponents .
Another way to write a square root is to the one-half power .
Polynomials (cont.) Solutions
- If an expression, written in simplest form, is a polynomial, then it can be classified by the degree and number of terms .
- The degree of a polynomial is the largest exponent when there is a single variable, or the largest sum of the exponents of the variables in a multivariate polynomial.
- A multivariate polynomial is a polynomial with two or more variables.
- With multivariate polynomials, add the exponents to find the largest sum even though the bases are not the same.
Degree | Classification |
| 0 | constant |
| 1 | linear |
| 2 | quadratic |
| 3 | cubic |
| 4 | quartic |
| 5 | quintic |
| n | nth degree |
Number of Terms | Classification |
| 1 term | monomial |
| 2 terms | binomial |
| 3 terms | trinomial |
| n-terms | polynomial with n-terms |
Example 2
Classify the polynomial expression by the degree and number of terms.
Expression A is a 4th degree, or quartic polynomial with 4 terms.
1st term exp:
2nd term:
3rd term:
Expression B is a 5th degree trinomial, or quintic trinomial.
1st term:
2nd term:
3rd term:
Expression C is a 9th degree trinomial.
Example 3
Determine whether each expression is a polynomial. If it is a polynomial, state the degree of the polynomial.
No, expression A is not a polynomial because the absolute value of a variable is being taken.
Yes, expression B is a polynomial.
The degree is 9.
Yes, expression C is a polynomial because the 4 is the only value under the radical.
The degree is 12.
- Item 1
- Item 2
- Item 3
- Item 1
- Item 2
- Item 3
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- Item 3