Summary: Polynomial Basics

Key Equations

Key Concepts

• A polynomial is a sum of terms each consisting of a variable raised to a nonnegative integer power. The degree is the highest power of the variable that occurs in the polynomial. The leading term is the term containing the highest degree, and the leading coefficient is the coefficient of that term.
• We can add and subtract polynomials by combining like terms.
• To multiply polynomials, use the distributive property to multiply each term in the first polynomial by each term in the second. Then add the products.
• FOIL (First, Outer, Inner, Last) is a shortcut that can be used to multiply binomials.
• Perfect square trinomials and difference of squares are special products.
• Follow the same rules to work with polynomials containing several variables.

Glossary

binomial

a polynomial containing two terms

coefficient

any real number [latex]{a}_{i}[/latex] in a polynomial of the form [latex]{a}_{n}{x}^{n}+\dots+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}[/latex]

degree

the highest power of the variable that occurs in a polynomial

difference of squares

the binomial that results when a binomial is multiplied by a binomial with the same terms, but the opposite sign

leading coefficient

the coefficient of the leading term

leading term

 the term containing the highest degree

monomial

a polynomial containing one term

perfect square trinomial

the trinomial that results when a binomial is squared

polynomial

a sum of terms each consisting of a variable raised to a nonnegative integer power

term of a polynomial

any [latex]{a}_{i}{x}^{i}[/latex] of a polynomial of the form [latex]{a}_{n}{x}^{n}+\dots+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}[/latex]

trinomial

a polynomial containing three terms

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