Polynomial Test Review

Standard Form and Naming

100

Give the degree of the monomial:   12x³y⁵

8

200

Name this polynomial:

5x⁵y² - 2x³y³ 

7th degree binomial

300

Put in standard form in relation to x AND give the name of the polynomial:

12x - 2x⁴y + 9x⁵y² - 10x³

9x⁵y² - 2x⁴y - 10x³ + 12x

degree: 7th degree polynomial

400

Put in standard form in relation to x and name it!

45x³y⁷ - 27x⁶y⁴ + 36x⁵y³

-27x⁶y⁴ + 36x⁵y³ + 45x³y⁷

10th degree trinomial

500

Name this polynomial

-6xy² +8x² - 2y²

cubic trinomial

Combining

100

4x² + 5x - 12 + 2x² - 8x - 1

6x² - 3x - 13

200

3x² + 2x - 4 - 3 - 10x + 5x²

8x² - 8x - 7

300

(10x⁵ - 4x³ - 2x⁴ - 9) - (6x² - 3x⁴ + 8x⁵)

2x⁵ + x⁴ - 4x³ - 6x² - 9

400

-(4x³ - 2x² + 5) - (2x³ + 5x² - 8)

-6x³ - 3x² + 3

500

7x³ + 2x² - 4x - (3x³ + 2x - 5x²)

4x³ + 7x² - 6x

GCF and Shortcuts

100

Factor:  x² - 144

(x + 12)(x - 12)

200

Find the product:  (3x - 5)²

9x² - 30x + 25

300

Factor out the GCF:     20x⁵y³ - 48x²y⁴ + 16xy

4xy(5x⁴y² - 12xy³ +4)

400

Factor out the GCF:     45x³y⁷ - 27x⁶y⁴ + 36x⁵y³

9x³y³(5y⁴ - 3x³y + 4x²)

500

Find the product:   (2x² + 4y²)²

4x⁴ + 16x²y² + 16y⁴

FOIL

100

(x - 8)(x - 4)

x² -12x + 32

200

(4x - 6)(6x + 2)

24x² - 28x - 12

300

(2x - 7)(4x + 8)

8x² - 12x - 56

400

(3x⁴ + 2y²)(5x⁴ - 4y²)

15x⁸ - 2x⁴y² - 8y⁴

500

Write the product of three consecutive even integers. Be sure your product is in standard form

n(n + 2)(n + 4)

n³ + 6n² + 8n

Factoring

100

x² + 3x - 54

(x + 9)(x - 6)

200

2x² - 7x - 4

(2x + 1)(x - 4)

300

6x² + 5x - 4

(3x + 4)(2x - 1)

400

The area of a rectangle is  2x² + x - 15 in²

Find the dimensions AND the perimeter

2x - 5 in by x + 3 in

Perimeter is 6x - 4 in

500

Use factoring to reduce:

(x^2 - 2x - 48)/(x^2 - 5x - 24)

(x + 6)/(x + 3)