Built from whole-number powers

Is 4/x + 3 a polynomial? Slide the power and see.

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".

• 7x has power 1. It is in.
• x² has power 2. It is in.
• 5 has power 0. It is in. So is x⁰, 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.

√9 is just the number 3. A root over a plain number is fine.

Try the lab to finish this lesson.