Built from whole-number powers
Is 4/x + 3 a polynomial? Slide the power and see.
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The rule
No. The letter in 4/x + 3 is under a division.
A polynomial is a sum of terms. A term is one part of the sum. Every letter in every term has a whole-number power.
The power can be 0, 1, 2, 3 or more. Whole numbers do not include −1 or one half. A letter with no small number has power 1.
1/x means x to the power −1. √x means x to the power one half.
Call an expression "in" when every letter has a whole-number power. Otherwise call it "out".
7xhas power 1. It is in.x²has power 2. It is in.5has power 0. It is in. So isx⁰, which equals 1.
Three kinds of term fail the rule.
- A letter under a division, like
4/x. Its power is −1. - A letter under a root, like
√x. Its power is one half. - A letter in the power place (the small raised number), like
2ˣ.
| Expression | Power | In or out |
|---|---|---|
7x + 2 | 1 | in |
x/4 + 3 | 1 | in |
4/x + 3 | −1 | out |
x² + √9 | 2 | in |
√x + 1 | one half | out |
2ˣ + 1 | the letter | out |
√9 is just the number 3. A root over a plain number is fine.