Algebra · Quick Reference

Polynomials Cheat Sheet

Algebra I · Lesson 6/17

In one line: a polynomial is an expression built from variables raised to whole-number powers, combined with addition, subtraction, and multiplication — the workhorse expressions of algebra.

Key Ideas

1Polynomial Terminology. A monomial has one term (5x), a binomial has two (x+3), a trinomial has three (x^2+2x+1); polynomial covers all of these and more.

2Degree of a Polynomial. The highest exponent on the variable in the expression. x^3 + 2x - 5 has degree 3.

3Adding and Subtracting Polynomials. Combine like terms (matching variable parts) just as with simpler expressions.

4Multiplying Polynomials. Use the distributive property, multiplying every term in the first polynomial by every term in the second (FOIL is a shortcut for two binomials: First, Outer, Inner, Last).

5Standard Form. Writing a polynomial with terms in order from highest to lowest degree.

Worked Examples

Add (3x^2 + 2x - 1) + (x^2 - 5x + 4).

4x^2 - 3x + 3

Multiply (x + 3)(x + 5) using FOIL.

x^2 + 8x + 15

Find the degree of the polynomial 4x^5 - 3x^2 + 7.

Degree 5

Formulas

FOIL for (a+b)(c+d): a*c + a*d + b*c + b*d

Practice Yourself

Add (2x^2+3x) + (x^2-x+5).

3x^2+2x+5

Subtract (5x^2+2x) - (2x^2+4x).

3x^2-2x

Multiply (x+2)(x+4) using FOIL.

x^2+6x+8