Algebra 1 Ch 7 Polynomial Equations and Factoring

FOIL Method

A method for multiplying two binomials by finding the sum of the products of the First terms, Outer terms, Inner terms, and Last terms

polynomial long division

A method to divide a polynomial f(x) by a nonzero divisor d(x) to yield a quotient polynomial q(x) and a remainder polynomial r(x).

polynomial

A monomial or a sum of monomials.

monomial

A number, a variable, or a product of a number and one or more variables with whole number exponents.

standard form of a polynomial

A polynomial in one variable written with the exponents of the terms decreasing from left to right.

closed

When an operation performed on any two numbers in the set results in a number that is also in the set. Example: The set of integers is closed under addition, subtraction, and multiplication, but not under division.

repeated roots

Two or more roots of an equation that are the same number.

factored form

A polynomial that is written as a product of factors.

factored completely

A polynomial that is written as a product of unfactorable polynomials with integer coefficients.

trinomial

A polynomial with three terms

binomial

A polynomial with two terms

synthetic division

A shortcut method to divide a polynomial by a binomial of the form x-k.

roots

The solution of a polynomial equation.

degree of a monomial

The sum of the exponents of the variables in the monomial.

Zero-Product Property

If the product of two real numbers is 0, then at least one of the numbers is 0.

leading coefficient

The coefficient of the first term of the polynomial written in standard form.

degree of a polynomial

The greatest degree of the terms in a polynomial.

factoring by grouping

To use the Distributive Property to factor a polynomial with four terms.