POLYNOMIALS

Classifying Polynomials

100

-5x

Linear Monomial

200

7x^2 + 4x

Quadratic Binomial

300

5x + 1

Linear Binomial

400

-4x^2+11x-2

Quadratic Trinomial

500

4x^3-2x^2+10x^2-1

Cubic Trinomial

Multiply Monomials

100

6a*9a^2

54a³

200

6xy(-8x²y)

-48x³y²

300

-3ab*2a^2b^3

-6a³b⁴

400

8x²y(9xy)

72x³y²

500

(5x)²

25x²

Adding/ Subtracting

100

(x² + 3x - 1) + (2x² + 4x + 5) 

3x² + 7x + 4

200

(4x² + 5x - 1) - (x² + 2x - 7) 

3x² + 3x + 6

300

(x³ + 4x - 3) + (x² + 8) 

x³ + x² + 4x + 5

400

(x - 4) - (x + 4) 

-8

500

(x² + 5x + 26) - (5x + 3) 

x² + 23

Multiplying

100

(2x - 6)(-3x + 2)

-6x² +22x-12

200

(x - 5) (x + 5)

x² + 6x - 27

300

(x - 6)²

x² - 12x + 36

400

(2x - 3)(x²+5x+7)

2x³+7x²-x-21

500

(9+3x)(x+4x²-2)

12x³+39x²+3x-18

Factoring

100

Factor out GCF: 24x² - 18x + 12

GCF: 6

200

Factor: x² + 7x + 12 

(x + 3)(x + 4) 

300

Factor: x² - 16

(x + 4)(x - 4) 

400

Use the "X Method" to factor: 6x² + 13x - 5

(3x - 1)(2x + 5)

500

Factor: x² + 22x + 121 

(x + 11)(x + 11) = (x + 11)²

Area & Perimeter

100

A rectangular garden has a length and width represented by the following expressions: (x + 3) feet by (x + 2) feet. Find the expression that represents the perimeter. Simplify your expression and write
it in standard form.

2(x + 3) + 2(x + 2) = 2x + 6 + 2x + 2 = 4x + 8

200

A square picture has an area represented by the expression (x² + 12x + 36) square inches. Find the side length measure of the picture.

(x + 6) inches

300

A rectangular garden has the following dimensions: length = (4x + 7) feet and width = (2x + 3) feet. Find the expression that represents the garden's area. *Foil

Area = LW

(4x + 7)(2x + 3) = 8x² + 26x + 12 square feet

400

A square hole with side length (x + 2) inches is cut from a square piece of fabric with side length (x + 6) inches. Find the expression that represents the area of the reminaing material. 

(x + 6)² - (x + 2)²

500

The base of a triangle measures (2x + 6) meters and the height measures (x + 4) meters. Find the area of the triangle. (A = 1/2 B x H)

1/2 (2x + 6)(x + 4) = x² + 7x + 12