Polynomials

Classifying

100

What is the degree and leading coefficient for the following:

y³ + 4 - 57y⁵ - 9 + 33y²

Degree: 5

Leading Coefficient: -57

200

What is the name for the degree of the following:

4x²-5+8x³+x-7x⁴

Quartic

300

What is the name for the number of terms of the following:

2m + 6 + 5m - 11m²

-11m + 7m + 6

Trinomial

400

What is the name for the degree AND the number of terms:

18 - 9x⁶ - 20x

6th Degree Trinomial

500

What is the name for the degree AND the number of terms:

-15y² + 6y⁴ + 5y⁴ - 3y²

11y⁴ - 18y²

Quartic Binomial

Simplifying

100

(4v² + 7) + (2v² - 5v)

6v² - 5v + 7

200

(3u² + 7u - 6) + (2u² - 7u - 4)

5u² - 10

300

(-5n² + 3n - 6) - (n² + 4n + 7)

-6n² - n -13

400

(7xy² + 5 - x²y²) - (6x²y - 3x²y²)

2x²y² + 7xy² - 6x²y + 5

or

2x²y² - 6x²y +7xy² + 5

500

(9u + 7u² - 1) + (4 -5u² - 3u) - (-9u + 2 + 2u²)

15u + 1

Multiplying

100

(y - 2)(y + 5)

y² + 3y - 10

200

(5x - 2y)(5x - 7y)

25x² + 14y² - 45xy

or

14y² + 25x² - 45xy

300

(u - 3)(6u² - 2u + 5)

6u³ - 20u² + 11u - 15

400

(4w² + 3w + 7)(4w² - 5w - 1)

16w⁴ - 8w³ + 9w² - 38w - 7

500

(7u + 7y + 2)(6u - 2y + 5)

42u² + 28uy - 14y² + 47u + 31y + 10

Factoring

100

36 - 25v²

(6 + 5v)(6 + 5v)

200

4c³w² + 6c⁴w

2c³w(2w + 3c)

300

6x³ + 14x² + 9x + 21

(2x² + 3)(3x + 7)

400

y² + 4y - 12

(y - 2)(y + 6)

or

(y + 6)(y - 2)

500

16z² + 16z - 21

(4z - 3)(4z + 7)

More Factoring

100

6y³ + 2y⁴w -7y²w²

y²(6y + 2y² - 7w²)

200

2x³ - 128x

2x(x + 8)(x - 8)

300

5j³ - 2j² + 30j - 12

(j² + 6)(5j - 2)

400

x² - 10x + 21

(x - 7)(x - 3)

500

Find the roots!!

x² - 10x + 21 = 0

{7,3}