Exponent Rules and Polynomials

Exponent Rules

100

Use the product rule for exponents to multiply:

4x^3*5x^2

20x^5

200

Use the quotient rule for exponents to divide:

(x^2y^5)/(xy^3)

xy^2

300

Use the power rule to simplify:

(4x^2yz^3)^2

16x^4y^2z^6

400

Use the quotient rule and the negative exponent rule to simplify:

(2x^2y^4)/(8x^5y^5)

(1)/(4x^3y)

500

Use the exponent rules to simplify:

(x^3y^4)^3*(3xy^2)^2

9x^11y^16

Classifying Polynomials

100

Determine the degree of the following polynomial:

-3x^2+5x-1

Degree: 2

200

Is the following polynomial a monomial, binomial, or trinomial?

2xy-3x^2y

Binomial

300

Classify the polynomial by its degree and the number of terms:

-4x^4+3x^2-x

Quartic Trinomial

400

Classify the polynomial by its degree and the number of terms:

3x^2-x

Quadratic binomial

500

Classify the polynomial by its degree and the number of terms:

-2xy^2+4xy-3y^2+1

Cubic Polynomial with 4 Terms

Adding & Subtracting Polynomials

100

Add the following polynomials. Write your final answer in standard form.

(4x^2+4)+(19x^2-7)

23x^2-3

200

Add the following polynomials. Write your final answer in standard form.

(13x^2y-2x+1)+(9x^2y-7)

22x^2y-2x-6

300

Add the following polynomials. Write your final answer in standard form.

(-x^3+8x^2-5)+(10x^3-x^2+1)

9x^3+7x^2-4

400

Subtract the following polynomials. Write your final answer in standard form.

(3x+2)-(11x-6)

-8x+8

500

Subtract the following polynomials. Write your final answer in standard form.

(x^2-x+4)-(x^2+x-2)

-2x+6

Multiplying & Dividing Polynomials

100

Divide the polynomial by the monomial. 

(4x^3+2x^2-8x)/(2x)

2x^2+x-4

200

Multiply the polynomials. Write your final answer in standard form.

(9x+1)(6x+2)

54x^2+24x+2

300

Multiply the polynomials. Write your final answer in standard form.

(4x-1)^2

16x^2-8x+1

400

Divide the polynomial by the monomial. Write your final answer in standard form.

(40x^5y^3-8x^3y^2+48xy)/(4x^2y)

10x^3y^2-2xy+12/x

500

Multiply the polynomials. Write your final answer in standard form.

(2x-5)(3x^2-x+6)

6x^3-17x^2+17x-30

Factoring

100

Factor the polynomial

x^4-100y^2

(x^2+10y)(x^2-10y)

200

Factor the polynomial

8a^3+1

(2a+1)(4a^2-2a+1)

300

Factor the polynomial

8n^4-2n^2-1

(4n^2+1)(2n^2-1)

400

Factor the polynomial

10x^8y^2+80x^2y^5

10x^2y^2(x^2-2y)(x^4+2x^2y+4y^2)

500

Factor the polynomial

6b^3-3b^2+4b-2

(2b-1)(3b^2+2)