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Special Kinds of Polynomials

We know what you're thinking. Aren't all polynomials special? Aw. That's sweet, but stop kissing up.

There are special names for polynomials with certain numbers of terms.

  • A monomial is a polynomial with only one term, such as 3x, 4xy, 7, and 3x2y34.
  • A binomial is a polynomial with exactly two terms, such as x + 3, 4x2 + 5x, and x + 2y7.
  • A trinomial is a polynomial with exactly three terms, such as 4x4 + 3x3 – 2.

You can remember these three because a tricycle has three wheels, a bicycle has two wheels, and a monocycle, that almost worked.

Another special kind of polynomial is a quadratic polynomial, which is a polynomial of degree 2. Yes, "quad" usually means "4," but bear with us.

A quadratic polynomial looks like ax2 + bx + c, where a, b, and c are real numbers and a isn't zero (if a were zero, the polynomial would only have degree 1).

A 2nd degree polynomial is "quadratic." Shouldn't it be "biratic?" What's the good of these numerical prefixes if they're only going to keep changing them on us?

A valid question. The answer? "Quad" also means "square." Oooh...sneaky.

In a single-variable polynomial of degree 2, we're squaring the variable, so it makes sense to think of that polynomial as "quadratic." We'll cross our fingers and hope "quad" doesn't also mean a third thing.

The following polynomials are quadratic.

  • x2
  • -4x2 + 8
  • 5x2 + 6x – 1

The following polynomials are not quadratic.

  • x + 5
  • x4 + 6x2 + 2
  • 8

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