Polynomials

Unit 2: Algebra Investigation

MM1A2c: Add, subtract, multiply, and divide polynomials.

Essential Question:

How do you add and subtract polynomials?

What does each prefix mean?

mono

one

bi

two

tri

three

What about the prefix: poly?MANY

A polynomial is a monomial or a sum or difference of monomials. Each monomial called a term.

Important Note!An expression is not a polynomial if there is a variable

in the denominator.

Different Types of Polynomials

Monomial: number (1, 2, 3, …), variable (a, b, c, …) or the product of a number and one or more variable (2x, -4xyz,…)

Binomial: Two terms (2x + 4y, 3xz + 5)

Trinomial: Three terms (4a + 2ab + 7b)

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

1) 7y - 3x + 4

trinomial

2) 10x3yz2

monomial

3)

not a polynomial2

57

2y

y

Degree of a Monomial

• The sum of the exponents of the variables in the monomial. The degree of a nonzero constant term is 0.

Ex. 4x3y2

The degree of the monomial is “5”

Find the degree of each monomial.

1) 5x2

2

2) 4a4b3c

8

3) -3

0

Degree of a Polynomial

The greatest degree of its terms.

Ex. 6z3 + 7z2 – 3z7

The degree of the polynomial is “7”

Which polynomial is represented by?

X2

1

1

X

X

X

1. x2 + x + 1

2. x2 + x + 2

3. x2 + 2x + 2

4. x2 + 3x + 2

5. I’ve got no idea!

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

8x2 - 2x + 7

Degrees: 2 1 0

Which is biggest? 2 is the degree!

y7 + 6y4 + 3x4m4

Degrees: 7 4 8

8 is the degree!

Find the degree of x5 – x3y2 + 4

1. 0

2. 2

3. 3

4. 5

5. 10

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:

1) 8x - 3x2 + x4 - 4

x4 - 3x2 + 8x - 4

2) Put in descending order in terms of x:

12x2y3 - 6x3y2 + 3y - 2x

-6x3y2 + 12x2y3 - 2x + 3y

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

-2x + 3y - 6x3y2 + 12x2y3

4) Put in ascending order:5a3 - 3 + 2a - a2

-3 + 2a - a2 + 5a3

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

1. x4 + 4xy – x3y2– 2x2y3

2. – 2x2y3 – x3y2 + 4xy + x4

3. x4 – x3y2– 2x2y3 + 4xy

4. 4xy – 2x2y3 – x3y2 + x4