POLYNOMIAL Function:

• A polynomial is the monomial or the sum of monomials with all exponents as whole numbers and coefficients are all real numbers.

• Ex- x3+6x2+12x+8

Is it a polynomial?

a) 3 3f x x x

b)

c)

d)

4 23 2 5xf x x x x

4 16 2f x x x x

20.5 2f x x x

YES

NO

NO

YES

STANDARD FORM

The terms of a polynomial are in STANDARD FORM when:

• they are ordered from left to right in ______________ order; which means from the ____________ exponent to the ____________

decreasing largest

smallest

The _________exponent in the polynomial. It determines the _____________________.

Ex: The degree of –7x + 9 – 4x2 is ____ because ___ is the largest exponent in the polynomial.

largest

2

2

Classifying:

0 – Constant

1 – Linear

2 – Quadratic

3 – Cubic

4 - Quartic

Number of Zeros

DEGREE:

LEADING COEFFICIENT:

The ______________once in _________________.

CONSTANT:

The term _________________ a variable.

first coefficient

standard form

without

STANDARD FORM

a. Standard Form:

Degree:

Leading Coefficient:

Constant:

2 4 32x 4 3x 12x

4 3 23x 12x 2x 4 3

4,quartic 4

b. Standard Form:

Degree:

Leading Coefficient:

Constant:

3 x

x 3

1,linear

1

3

Some polynomials have SPECIAL NAMES that are determined by the following:

A. Their _________ or

B. Their _________ of terms

C. Look at the chart for an explanation.

degree

number

Polynomial # of Terms

Name by # of Terms

DEGREE Name by Degree

12

8x

4x2 + 3

5x3 + x2

3x2 – 4x + 6

7t4 – 7t + 3

1

1

2

2

3

MonomialMonomialBinomial

Binomial

Trinomial

0

1

2

3

2

Constant

Linear

Quadratic

Cubic

Quadratic3 Trinomial 4 Quartic

ADDING AND SUBTRACTING POLYNOMIALS

ADDING:•Combine like terms!

SUBTRACTING:•Distribute the negative•Combine like terms!

EX. 1

3 2 5 3 24 5 12 2 14y y y y y

5 3 212 2 9y y y

EX. 2

5 3 2 5 3 23 8 10 12 4 14 y y y y y y

5 3 215 4 24 y y y

EX. 3

2 27 8 4 11 2 14 n n n n

27 19 6 n n

EX. 4

2 4 410 7 6 14 4 14 k k k k k

4 22 10 7 14 k k k