Identify and Evaluate Polynomials
Learning Outcomes
- Identify a polynomial
- Evaluate a polynomial for given values
Identify a polynomial
The following table is intended to help you tell the difference between what is a polynomial and what is not.IS a Polynomial | Is NOT a Polynomial | Because |
Polynomials only have variables in the numerator | ||
Polynomials only have variables in the numerator | ||
Roots are equivalent to rational exponents, and polynomials only have integer exponents |
Example
Which of the following expressions is a polynomial? Select all that apply.Answer:
- is a polynomial.
- is not a polynomial because it contains a non-integer exponent.
- is a polynomial.
- is not a polynomial because it contains a negative exponent.
Monomials | Binomials | Trinomials | Other Polynomials |
Evaluate a polynomial
You can evaluate polynomials just as you can other kinds of expressions. To evaluate an expression for a value of the variable, you substitute the value for the variable every time it appears. Then use the order of operations to find the resulting value for the expression.Example
Evaluate for .Answer: Substitute for each x in the polynomial.
Following the order of operations, evaluate exponents first.
Multiply times , and then multiply times .
Change the subtraction to addition of the opposite.
Find the sum.
Answer
Example
Evaluate for .Answer: Substitute for each p in the polynomial.
Following the order of operations, evaluate exponents first and then multiply.
Add and then subtract to get .
Answer
In the following video we show more examples of evaluating polynomials for given values of the variable.
https://youtu.be/2EeFrgQP1hM