Add & Subtract Polynomials

Math Notebook & Pencil

Monomial

•Number, a variable, or the product of a number and one or variables with whole number exponents.

•The degree of a monomial is the sum of the exponents of the variables in the monomial. The degree of a nonzero constant term is 0. The constant 0 does not have a degree.

ExamplesMonomial Degree

10 0

3x 1

3x^2 2

3x^10 10

Not a Monomial Not a Monomial Reason

5 + x A sum is not a monomial

2/n Cannot have a variable in denominator

4^a Cannot have a variable exponent

Polynomial

•A monomial or a sum of monomials, each called a term of the polynomial.

•The degree of a polynomial is the greatest degree of its terms.

Leading Coefficient

•When a polynomial is written so that the exponents of a variable decrease from left to right, the coefficient of the term is called a leading coefficient

•2x^3 + x^2 -5x +12

Leading coefficient

Re-writing a Polynomial

•Write 15x-x^3 + 3 so that the exponents decrease from left to right.

•Label your leading coefficient, degree and constant.

Classifying Polynomials

•A polynomial with two terms is called a binomial.

•A polynomial with three terms is called a trinomial.

Examples

•Is this a polynomial?

•What degree?

Let’s look at 6n^4 -8^n

Adding Polynomials

•(2x^3 – 5x^2 + x) + (2x^2 + x^3 - 1)

•Solution:

Vertical Format: If a particular power of a the variable appears in one polynomial but not the other, leave a space in that column, or write the term with a coefficient of 0

Degree and Leading Coefficient

•Write 5y-2y^2 +9 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial.

Let’s Try

•(3x^2 +x-6) + (x^2 +4x + 10)

Let’s Try

•(4n^2 +5) – (-2n^2 +2n -4)

Let’s Try

•(4x^2 -3x+5) – (3x^2 –x- 8)