Polynomial Review

Getting to Know Polynomials

100

Name the polynomial based on its degree and number of terms.

100x² + 3

quadratic binomial

200

Simplify and write in standard form.

5 + 8y² - 12y² + 3y

-4y² + 3y + 5

300

Name the polynomial based on its degree and number of terms.

-9x⁴ + 8x³ - 7x + 1

fourth degree polynomial

400

Simplify and write in standard form.

7 - 2x + 3 + 5x + 4x²

4x² + 3x + 10

500

Name the polynomial based on its degree and number of terms.

5x³ + 2x - 8

cubic trinomial

"Add 'Sub, Poly!"

100

Find (2x² - 7x³ + 8x) + (-8x³ - 3x² + 4)

-15x³ - x² + 8x + 4

200

Find 

(3b - 8) + (7b + 4)

10b - 4

300

Find 

(-7a⁴ - a + 4a²) - (-8a² + a - 7a⁴)

12a² - 2a

400

Find the perimeter of a rectangle with length 3x - 1 and width x + 1.

8x

500

Find 

(5y² - 2y + 1) - (y² + y + 3)

4y² - 3y - 2

Product Power!

100

Find the product and write in standard form.

-5x³(2x³ - 4x² + 2)

-10x⁶ + 20x⁵ - 10x³

200

Find the product and write in standard form.

(2x + 1)(4x + 1)

8x² + 6x + 1

300

Find the product and write in standard form.

(2x - 7)(3x² - 4x + 1)

6x³ - 29x² + 30x - 7

400

Find the product and write in standard form.

(2x² - 3x)(-3x² + 4x - 2)

-6x⁴ + 17x³ - 16x² + 6x

500

A rectangular park is 6x + 2 ft long and 3x + 7 ft wide. In the middle of the park is a square turtle pond that is 8 ft wide. Find the area of the park that is not occupied by the turtle pond.

18x² + 48x - 50 ft²

Special products are my specialty

100

Find 

(5x - 3)²

25x² - 30x + 9

200

Find

(3x + 8)²

9x² + 48x + 64

300

Find

(3a - 4b)(3a + 4b)

9a² -16b²

400

Find

(x² - 2y)(x² + 2y)

x⁴ - 4y²

500

Find

(\frac{2}{5}x + \frac{1}{5})^2

(4/25)x² + (4/25)x + (1/25)

It's my first time factoring...

100

Factor out the GCF.

12x² - 15x

3x(4x - 5)

200

Factor out the GCF.

-4y⁴ + 6y² - 14y

-2y(2y³ - 3y + 7)

300

Factor out the GCF.

24x³y² - 30x²y³ + 12x²y⁴

6x²y²(4x - 5y + 2y²)

400

Factor out the GCF.

100a⁷b⁵ - 150a⁸b³

50a⁷b³(2b² - 3a)

500

The area of a rectangle is 6x² - 18x ft². Use factoring to find the length and width of the rectangle.

6x ft and x - 3 ft

The leading coefficient is 1? Yes, please!

100

Factor 

x² - 2x - 8

(x + 2)(x - 4)

200

Factor 

x² - 12x+ 27

(x - 9)(x - 3)

300

Factor 

x² - 16xy + 28y²

(x - 14y)(x - 2y)

400

Factor 

x² + 16x + 48

(x + 12)(x + 4)

500

Factor 

x² + 15xy +54y²

(x + 9y)(x + 6y)

I like to hang out in my grouping

100

Factor

6x² - 25x - 14

(3x - 14)(2x + 1)

200

Factor

12x² + 16x + 5

(6x + 5)(2x + 1)

300

Factor

24x³ - 10x² - 4x

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

400

Factor

2x² + 9xy + 10y²

(2x + 5y)(x + 2y)

500

The area of a rectangle is 6x² + 7x - 5 ft². Factor to find the length and width of the rectangle.

3x + 5 ft and 2x - 1 ft

You are a special factoring case to me

100

Factor

x² - 25

(x - 5)(x + 5)

200

Factor

100x² - 36

(10x - 6)(10x + 6)

or

4(5x + 3)(5x - 3)

300

Factor

121x² + 110x + 25

(11x + 5)²

400

Factor

-3x³ + 18x² - 27x

-3x(x - 3)²

500

Factor

 x^2 - \frac{49}{100} 

(x - \frac{7}{10})(x + \frac{7}{10})