9.1 adding and subtracting polynomials. the terms of a polynomial may appear in any order. however,...

9.1 Adding and Subtracting PolynomialsObjective: Classify of polynomial by

degree and terms. Add and subtract

polynomials.

Standard Addressed: 2.8.11.S.

Analyze properties and relationships

of polynomials.

A monomial is a numeral, a variable, or the product of a numeral and one or more variables.

A monomial with no variables, such as –1 or , is called a constant.

A coefficient is the numerical factor in a monomial.

A polynomial is a monomial, or a sum or difference of terms that are monomials.

A polynomial with two terms is a binomial.

A polynomial with three terms is a trinomial.

The degree of a polynomial in one variable is determined by the exponent with the greatest value within the polynomial.

The terms of a polynomial may appear in any order. However, in standard form, the terms of a polynomial are ordered from left to right in descending order, which means from the greatest exponent to the least.

Ex. 1 a.

Ex. 1 b. Write in standard form.

4x5 + 2x3 – 3x

Some polynomial expressions have special names that are determined either by their degree or by the number of terms, as illustrated in the table.

Ex 1. Classify each polynomial by degree and by number of terms.

First, combine Like terms with the same letter and exponent power.

Second, what is the highest exponent and name it by the degree.Third, count how many terms there are and name it.a.2x3 - 3x + 4x3 b. –2x3 + 3x4 + 2x3

+ 5

c. x2 + 4 - 8x - 2x3 d. 3x3 + 2 – x3 – 6x5

e. 5x + 2x3 + 4x2 f. x5 – 4x3 - x5 + 3x2 + 4x3

6x3 – 3x Cubic Binomial 3x4 + 5 Quartic Binomial

Cubic Polynomial 2x3 – 6x5 + 2 Quintic Trinomial

Cubic Trinomial 3x2 Quadratic Monomial

Adding PolynomialsPolynomials can be added in vertical and horizontal form. In vertical form, align the like terms and add. In horizontal form, regroup like terms and add.

Ex. 3

Ex. 4a. (-2x2 – 3x3 + 5x + 4) + (-2x3 + 7x – 6)

-5x3 – 2x2 + 12x – 2

Ex. 5

Subtracting PolynomialsRecall that subtraction can be modeled by adding the opposite.

Ex.6

Ex 3. Find the difference and write

it from highest to lowest power.

Ex. 7 (-6x3 – 6x2 + 7x – 1) – ( 3x3 – 5x2 – 2x + 8)

-9x3 – x2 + 9x – 9