Polynomials

Classify

100

What is the degree of this polynomial?

7x³ + 4x² - 3x - 1

Degree 3 

*will also accept cubic

200

How many terms does a binomial have?

Bonus: write an example of a binomial

2

300

Why is this not a polynomial? Choose the best answer.

5y(12y³ + 9)

A. A variable is being divided

B. It isn't simplified

C. The teacher said so

D. It has y, not x

B. It isn't simplified

400

Classify this polynomial:

n⁴ + 3 + n

Trinomial degree 4 (or quartic trinomial)

500

What is the leading coefficient in this expression?

6x² + 7x³ + 9x

7

Multiply

100

(3x²)(4x² - 5x + 7)

12x⁴ - 15x³ + 21x²

200

(7x - 4)(8x +9)

56x² + 31x - 36

300

(3x + 2)(4x² - 7x + 5)

12x³ - 13x² + x + 10

400

(2x² - 5x)(9x² + 6x + 4)

18x⁴ - 33x³ - 22x² - 20x

500

(x + y)(x + z)

x² + zx + yx + yz

Add/Subtract

100

(6t -3) + (4t + 5)

10t + 2

200

(14m + 5) - (-2m + 1)

16m + 4

300

(3x³ - 7x + 2) + (2x² + x - 5)

3x³ + 2x² - 6x - 3

400

(-4x² + 9x) + (-x - 3) - (8x² + 4x - 7)

-12x² + 4x + 4

500

(x⁴ - 8x + 3) - (x⁴ - 7x + 3)

Simplify your answer

x

Factor out Monomial

100

What is the greatest common factor of 24y² and 54y

6y

200

Factor 16m - 20m³

4m(4 - 5m²)

300

Factor 15w³ - 9w² + 21w

3w(5w² - 3w + 7)

400

Factor 10k³x² + 6k³x + 16k²x

2k²x(5kx + 3k + 8)

500

Factor (-8a³b⁴ - 32ab²)

-8ab²(a²b² + 4)

Factor Quadratic

100

Factor into two binomials: 

x² + 14x + 24

(x + 2)(x + 12)

200

Factor into two binomials:

x² + 6x - 27

(x + 9)(x - 3)

300

Factor into two binomials:

y² - 36

BONUS: what is the special name we give to expressions like this?

(y + 6)(y - 6)

BONUS: difference of squares

400

Factor into two binomials:

k² - 7k -18

(k + 2)(k - 9)

500

Factor into two binomials:

5x² + 16x + 3

(x+3)(5x+1)