Exponent Rules and Polynomials

Exponent Rules

100

Use the product rule for exponents to multiply:

4x^3*5x^2

20x^5

200

Use the product rule to multiply:

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

x^3y^8

300

Use the power rule to simplify:

(4x^2yz^3)^2

16x^4y^2z^6

400

Use the product rule to multiply:

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

16x^7y^9

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

What is the leading coefficient of the following polynomial?

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

-4

400

What is the degree and leading coefficient of the following polynomial?

3x^2-x

Degree: 2

Leading Coefficient: 3

500

What is the degree of the following polynomial?

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

3

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 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.

(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

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

(7x+4)(7x-4)

49x^2-16

500

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

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

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