Polynomial Terminology

Pre-Calculus · Axiom Academy

Term, coefficient, degree, leading term, and standard form — the working vocabulary you need before doing anything with polynomials. 1. What Counts as a Polynomial? A polynomial is built from variables and numbers using only addition, subtraction, and multiplication, where every variable carries a whole-number exponent (0, 1, 2, 3, …). That one rule about exponents is the gatekeeper. The animation runs each candidate's exponent through the gate: a whole number passes; a negative, a fraction, or a variable hiding in a denominator gets turned away. where the coefficients are numbers and n is a whole number. 3x^4 - 2x^2 + 5x - 7 · x^2 + 1 · 5 (a constant counts — it's 5x^0 ). (variable in a denominator) · (fractional exponent) · x^ -2 + 1 (negative exponent). A term is one chunk of a polynomial — the pieces separated by + and - signs. Each term splits into a coefficient (the number out front, sign included) and a variable part with an exponent. The animation pulls the single term -2x^ 3 apart so you can see exactly which piece is which, then names the term's degree as that exponent. The numerical factor in front. In -2x^3 it is -2 — the minus sign belongs to it. The exponent on the variable. -2x^3 has degree 3 ; 4x^5 has degree 5 . -x means : the coefficient is -1 and the degree is 1 , even though neither is written. A lone number like 7 is 7x^0 — degree 0 , since x^0 = 1 . 3. Degree, Leading Term & Leading Coefficient

This is the written version of the interactive lesson above. See the full Pre-Calculus course.