Polynomials part 1- Vocabulary and Understanding

Algebra 1 Tutorial

Polynomials part 1- Vocabulary and Understanding

Intro

A polynomial is an expression that consists of variables and coefficients. The expression will only consist of operations of addition, subtraction, and multiplication, as well as exponents that are non-negative integers. There are 4 types: 1) monomial 2) binomial 3) trinomial 4) polynomial. Examples:
1) 4x
2) 5x+3y
3) 3x^2+2x+2
4) x^5-3x^2+x-5

Notice that the variable with the largest exponent will always come first, followed by the next largest exponent. If there is no variable, it will be at the very end. Use the chart below to help breakdown a polynomial.

polynomial

This is the format that we write polynomials in:
equation
The purpose of this format is to help understand the order in which the equation should be written. It also shows that the equation will equal zero, this way we can solve for x. We will go over solving polynomials in the next tutorial.

Polynomials are measured in degrees. The degree of the expression is based on the largest exponent.
degree

These are the basics of polynomials which will help us solve more complex equations, graph them, and interpret graphs so to write equations in the following tutorials.

Sample Problem

1)Which is a polynomial?
a) 4x+3x-5y
b) 3x+55
c) 4x^3-5y^7
d) x^6+11x^2-x-1

2) Given the expression 6x^7+3x^3-x+7, give the following:
a) Terms
b) factors
c) coefficients
d) exponents
e) constants

3) List the degree of the following equations:
a) x-22
b) x^2+9
c)x^24-26x^12+x-4

Solution

1) d.
Option a is technically a binomial because 4x+3x=7x, making the equation 7x-5y. Option b, there are not enough terms. Option c is also a binomial.

2) a) The terms are 6x^7, 3x^3, -x, and 7.
b) The factors are 6 and x, 3 and x, -1 and x, and 7. Notice that -x=-1x
c) The coefficients are 6, 3, -1, and 7
d) The exponents are 7, 3, and 1. Remember, although -x is alone we can assume it is actually to the power of 1.
e) The constant is 7.

3) a)1, even though x is alone we assume it is to the power of one
b) 2, since x is to the second power
c) 24, the largest exponent is 24. Do not confuse the coefficient with the exponent.



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