# Polynomials

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### Objectives The student will be able to::

Objectives The student will be able to: 1. find the degree of a polynomial. 2. arrange the terms of a polynomial in ascending or descending order. SOL: none Designed by Skip Tyler, Varina High School

### What does each prefix mean?:

What does each prefix mean? mono one bi two tri three

What about poly? one or more A polynomial is a monomial or a sum/difference of monomials. Important Note!! An expression is not a polynomial if there is a variable in the denominator.

### State whether each expression is a polynomial. If it is, identify it.:

State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x 3 yz 2 monomial 3) not a polynomial

### Which polynomial is represented by :

Which polynomial is represented by X 2 1 1 X X X x 2 + x + 1 x 2 + x + 2 x 2 + 2x + 2 x 2 + 3x + 2 I’ve got no idea!

### The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial.:

The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. 1) 5x 2 2 4a 4 b 3 c 8 -3 0

### To find the degree of a polynomial, find the largest degree of the terms.:

To find the degree of a polynomial, find the largest degree of the terms. 1) 8x 2 - 2x + 7 Degrees: 2 1 0 Which is biggest? 2 is the degree! 2) y 7 + 6y 4 + 3x 4 m 4 Degrees: 7 4 8 8 is the degree!

### Find the degree of x5 – x3y2 + 4:

Find the degree of x 5 – x 3 y 2 + 4 0 2 3 5 10

### A polynomial is normally put in ascending or descending order.:

A polynomial is normally put in ascending or descending order. What is ascending order? Going from small to big exponents. What is descending order? Going from big to small exponents.

### Put in descending order::

Put in descending order: 8x - 3x 2 + x 4 - 4 x 4 - 3x 2 + 8x - 4 2) Put in descending order in terms of x: 12x 2 y 3 - 6x 3 y 2 + 3y - 2x -6x 3 y 2 + 12x 2 y 3 - 2x + 3y

### 3) Put in ascending order in terms of y: 12x2y3 - 6x3y2 + 3y - 2x:

3) Put in ascending order in terms of y: 12x 2 y 3 - 6x 3 y 2 + 3y - 2x -2x + 3y - 6x 3 y 2 + 12x 2 y 3 Put in ascending order: 5a 3 - 3 + 2a - a 2 -3 + 2a - a 2 + 5a 3

### Write in ascending order in terms of y: x4 – x3y2 + 4xy – 2x2y3:

Write in ascending order in terms of y: x 4 – x 3 y 2 + 4xy – 2x 2 y 3 x 4 + 4xy – x 3 y 2 – 2x 2 y 3 – 2x 2 y 3 – x 3 y 2 + 4xy + x 4 x 4 – x 3 y 2 – 2x 2 y 3 + 4xy 4xy – 2x 2 y 3 – x 3 y 2 + x 4