Math 4.1 - 4.2 terms

Polynomial function

a function in the form of f(x) = ax^b + bx^m +… where all the exponents are whole numbers and the coefficients are all real numbers

Common Polynomial are in what form

Standard Form (exponents are arranged in order from highest to lowest)

Common Polynomial Degrees

0, 1, 2, 3, 4

Degree is 0 (what is the type)

Degree: 0

Type: Constatant

Example: f(x) = 3x⁰ OR f(x) = -14

Degree is 1 (what is the type)

Degree: 1

Type: linear

Example: f(x) = 2x¹ + 3 OR f(x) = 3x - 5

Degree is 2 (what is the type)

Degree: 2

Type: quadratic

Example: f(x) = 3x² + 2x - 7

Degree is 3 (what is the type)

Degree: 3

Type: cubic

Example: f(x) = 2x³ + 8

Degree is 4 (what is the type)

Degree: 4

Type: quartic

Example: f(x) = x⁴ + 5x + 6

Leading coefficient (LC)

the number next to the variable with the highest exponents

what is the End Behavior when the Degree is odd and the LC is positive

As x —> ♾, y —> - ♾

As x —> - ♾, y —> ♾

what is the End Behavior when the Degree is odd and the LC is negative

As x —> ♾, y —> ♾

As x —> - ♾, y —> - ♾

what is the End Behavior when the Degree is even and the LC is negative

As x —> ♾, y —> - ♾

As x —> - ♾, y —> - ♾

what is the End Behavior when the Degree is even and the LC is positive

As x —> ♾, y —> ♾

As x —> - ♾, y —> ♾

adding polynomials

You take look at the exponents to see which numbers get added together in standard form (when adding DO NOT add the exponents together, they stay their original number)

Ex: (2x³ + x² - 3x + 4) + (x³ + 7x² - 2) = 3x³ + 8x² - 3x + 2

subtracting polynomials

you can either add them and change the signs of everything or subtract them. Like adding polynomials you can only add the number together if they have the same coefficient. (DO NOT add the coefficients together. They stay the same as their original number)

Ex: (3x³ + 5x² - x + 8) - ( 5x³ - 4x² - 3x + 1)

*change to addition* —> (3x³ + 5x² - x + 8) + ( -5x³ + 4x² + 3x - 1)

*add them together based on exponents* —> -2x³ + 9x² + 2x + 7

Multiplying polynomials

Have to multiply each term on both sides by each other and when you are multiplying polynomials you have to add the exponents

Ex: (x-2)(2x² - 3x + 5)

1. Multiply (x-2)(2x² -3x + 5)

2. Multiply (x-2)(2x² -3x+ 5)

3. Add like terms 2x³ -3x² + 5x -4x² +6x -10

4. Answer: 2x³ -7x² + 11x - 10