Exponent Rules and Polynomials

Exponent Rules

100

Use the product rule for exponents to multiply:

4x^3*5x^2

20x^5

200

Use the power rule to simplify:

(4x^2yz^3)^2

16x^4y^2z^6

300

Use the quotient rule for exponents to divide:

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

xy^2

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

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

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

Quartic Trinomial

300

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

2xy-3x^2y

Binomial

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.

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

9x^3+7x^2-4

300

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

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

22x^2y-2x-6

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 Polynomials

100

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

-3x(2x^2+4)

-6x^3-12x

200

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

(7x^2-5x+8)3x

21x^3-15x^2+24x

300

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

(4x)(6x^2+3x+2)

24x^3+12x^2+8x

400

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

-(7x^5+8x^2-3x^5)

-4x^5-8x^2

500

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

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

6x^3-2x^2+12x

Dividing Polynomials

100

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

(5x^2+25x)/(5x)

x+5

200

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

(9x^3-15x^2+27x)/(3x)

3x^2-5x+9

300

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

(-12a^5+30a^4+21a^3)/(3a^2)

-4a^3+10a^2+7a

400

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

(18x^4-10x^2+6x^7)/(2x^2)

3x^5+9x^2-5

500

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

(4x^3y^2+8xy^2-12x^2y^3)/(4xy)

x^2y+2y-3xy^2