Polynomials Review!

Classifying Polynomials

100

Classify This Polynomial:

x² + 5

Quadratic Binomial

200

Classify This Polynomial:

-8x

Linear Monomial

300

Classify This Polynomial

x⁴ - 6x + 2

Quartic Trinomial

400

Classify This Polynomial:

6x⁷ + 3x

7th Degree Binomial

500

Classify This Polynomial:

9x⁴ - 8x³ + x² + 2x + 17

Quartic Polynomial

End Behavior

100

Fill in the blanks for the following:

f(x) = 3x³ + x² + 4

x --> ∞, f(x) --> _________.

x --> -∞, f(x) --> __________.

x --> ∞, f(x) --> ∞.

x --> -∞, f(x) --> -∞.

200

Fill in the blanks for the following:

f(x) = -x² + x

x --> ∞, f(x) --> _________.

x --> -∞, f(x) --> __________.

x --> ∞, f(x) --> -∞.

x --> -∞, f(x) --> -∞.

300

Fill in the blanks for the following:

f(x) = -x + 3

x --> ∞, f(x) --> _________.

x --> -∞, f(x) --> __________.

x --> ∞, f(x) --> -∞.

x --> -∞, f(x) --> ∞.

400

Fill in the blanks for the following:

f(x) = (x - 1)(x + 5)

x --> ∞, f(x) --> _________.

x --> -∞, f(x) --> __________.

x --> ∞, f(x) --> ∞.

x --> -∞, f(x) --> ∞.

500

Fill in the blanks for the following:

f(x) = x + 3 -4x⁴ + 8x³

x --> ∞, f(x) --> _________.

x --> -∞, f(x) --> __________.

x --> ∞, f(x) --> -∞.

x --> -∞, f(x) --> -∞.

Adding and Subtracting Polynomials

100

Add the Polynomials

(4x - 9) +(x - 4)

5x - 13

200

Add the Polynomials:

(x² +3x + 5) + ( -x² +6x)

9x + 5

300

Add the Polynomials:

(x³ -1 + x² + 2x) + (1 - 2x - 4x³ + 2x²)

-3x³+3x²

400

Subtract the Polynomials:

(-x² - 5) - (-3x² -x -8)

2x² + x +3

500

Subtract the Polynomials:

(x² + 6x³ - 4) - (5x³ + 7x -3x²)

x³ + 4x² -7x -4

Multiplying Polynomials

100

Multiply the Polynomials:

2x (x³ - 8x)

2x⁴ - 16x²

200

Multiply the Polynomials:

3x² (2x⁴ + 4)

6x⁶ + 12x²

300

Multiply the Polynomials:

(x - 8)(2x + 3)

2x² - 13x - 24

400

Multiply the Polynomials:

(4x + 3)(x² - 6x + 9)

4x³ - 21x² + 18x + 27

500

Multiply the Polynomials:

(3x - 5)(2x² + 7x - 4)

6x³ + 11x² - 47x + 20

?? Mystery ??

100

What is the name for the highest exponent on a variable term in a polynomial?

Degree

200

What is the name for the number in front of the term containing the degree?

Leading Coefficient

300

Give 3 reasons why this isn't a polynomial:

x^1/2 - 2x + 3x^-1 + 6^x - 8

- an x has a fractional exponent

- an x has a negative exponent

- there is a term where x is in the exponent

400

Rewrite This Polynomial in Standard Form:

3 + 6x² + 4x⁵ + 9x

4x⁵ + 6x² + 9x + 3

500

Describe the zeros and the end behavior of this function:

f(x) = (x - 2)(x - 1)(x + 4)(x + 7)

- Zeros: x = 2, 1, -4, -7

- End Behavior: Positive Even / Both Ends Go Up