Algebra 1 Chapter 5 Some operations with polynomials and radicals

20 terms

Polynomial

An expression that has no operations other than addition, subtraction, and multiplication by or of the other variables

Degree

The exponent of the highest power of the variable

Linear

A polynomial in the first degree

A polynomial in the second degree

Cubic

A polynomial in the third degree

Multiplying Two Binomials

1. Multiply each term of one binomial by each term of the other
2. Combine the like terms

Factoring a Polynomial

This means to transform a polynomial to a product of two or more factors

Prime Polynomial

is a polynomial whose only factors are itself and one

Coefficient of the highest degree term

Conjugate Binomials

These are binomials that are the same except for the sign between the terms
For example, 3x+5 and 3x-5 are conjugate binomials.

Difference of Two Squares

The factors of this are conjugate binomials.
For example, a^2 - b^2 = (a+b)(a-b)

Binomial Square Pattern

1) square the first term.
2) add twice the product of the two terms.
3) add the square of the last term.

Trinomial Square

The quadratic that is the result of squaring a binomial

Square Root

The square root of n is the number that gives n for the answer if it is simplified.

If n is not negative, (√n)^2 = n

An expression that has a root, such as √49, is called a radical

Rational Number

A number that can be written as a ratio of two integers

Irrational Number

A real number that cannot be written as a ratio of two integers

Closure

A given set of given numbers is closed under an operation if there is just one answer and the answer is in the given set whenever the operation is performed with the numbers in that set

Closure Under Multiplication

The set of real numbers is closed under multiplication