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.