Polynomials

Classifying Polynomials

100

A polynomial that has three terms is called a _____________

Trinomial

200

Determine the degree of the following:

x² + x - 2

2

300

Determine the name of the following polynomial:

x³yz² - 2xy⁵

Binomial

400

Determine the degree and name of the polynomial.

x⁵y²

7th Degree Monomial

500

Determine the degree and name of the polynomial.

a⁴b³c - 2a²b³

8th Degree Binomial

Simplifying Polynomials

100

Simplify:

(x + 3) + (x² - 4)

x² + x - 1

200

Simplify:

-7x² (4x² + 6x - 7)

-28x⁴ - 42x³ + 49x²

300

Simplify:

(5x + 3y)²

25x² + 30xy + 9y²

400

Simplify:

(-4x² - 3x - 4) - (7x² + 9x - 6) + (-6x² - 9x + 2)

-17x² - 21x + 4

500

Simplify:

(2x² - 3x - 7)(7x + 5)

14x³ - 11x² - 64x - 35

Factoring (GCF)

100

Factor out the GCF:

2x + 10

2(x + 5) 

200

Factor out the GCF:

3x³ - 6x² + 12x

3x(x² - 2x + 4)

300

Factor out the GCF: 

14x⁵y⁶z⁷ + 35x⁸y⁷z⁶

7x⁵y⁶z⁶ (2z + 5x³y)

400

Factor out the GCF:

8x⁵y³ - 12x³y⁵ + 20xy⁷

4xy³ (2x⁴ - 3x²y² + 5y⁴)

500

Factor out the GCF:

24x³y⁴z⁷ - 4x⁹y⁹

4x³y⁴ (6z⁷ - x⁶y⁵)

Factoring (a = 1)

100

Factor:

x² + 5x + 6

(x + 2)(x + 3)

200

Factor:

x² - x - 20

(x - 5)(x + 4)

300

Factor:

x² + 8xy + 16y²

(x + 4y)(x + 4y) 

400

Factor:

x² - 100

(x + 10)(x - 10)

500

Factor:

x² + 14xy - 51y²

(x - 3y)(x + 17y)

Factoring (a > 1)

100

Factor completely:

2x² + 26x - 60

2(x + 15)(x - 2)

200

Factor completely:

4x² - 81

(2x + 9)(2x - 9)

300

Factor completely:

3x² + 34x - 24

(3x - 2)(x + 12)

400

Factor completely:

75 - 27x²

3(5 + 3x)(5 - 3x)

500

Factor completely:

12x² - 22x + 10

2(6x - 5)(x - 1)