Polynomial Vocabulary

Algebra 1 · Axiom Academy

The names behind every polynomial — term, coefficient, degree, and standard form — shown as the parts light up and sort themselves into place. A polynomial is an algebraic expression made of one or more terms — each a number, a variable, or a product of numbers and variables raised to whole-number exponents. Watch one assemble from its pieces: each block snaps onto the line, joined by + and - signs. Each piece of a polynomial separated by a + or - is a term , and the number multiplying the variable in a term is its coefficient . Watch 4x^3 - 7x^2 + 2x - 9 split apart at its signs — the sign travels with the term, so its coefficient carries that sign too. The degree of a term is the exponent on its variable; the degree of the polynomial is the highest of those. Watch each term of 5x^4 + 3x^2 - 8x + 1 grow a bar as tall as its exponent — the tallest bar wins, and that is the degree. Standard form writes a polynomial with its terms in descending order of degree, highest power first. Watch the scrambled 7 - 2x + 5x^3 + 3x^2 sort itself: each term carries its degree, and they slide into place from highest to lowest. Standard form (degrees 3, 2, 1, 0 ): We name a polynomial two ways at once: by its degree and by its number of terms . Watch 2x^2 - 5x + 3 travel down both tracks together — one finds its degree-name, the other counts its terms — and the two names combine. 0 constant · 1 linear · 2 quadratic 3 cubic · 4 quartic · 5 quintic 1 term monomial · 2 terms binomial

This is the written version of the interactive lesson above. See the full Algebra 1 course.