Exponent Rules and Polynomials

Exponent Rules

100

Use the product rule for exponents to multiply:

4x^3 "x"  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 "x"  (3xy^2)^2

9x^11y^16

Degree of Polynomials

100

Determine the degree of the following monomial:

-3x^2

Degree: 2

200

What is the degree of this polynomial?

2x^3 + 5x - 6

Degree: 3

300

Determine the degree of the second term:

-4x^4+3x^2y-xz

Degree: 3

400

What is the degree of the following polynomial?

(3x^2-x)xy-5xy^2 

Degree: 4

500

Determine the degree of the following polynomial:

(-2xy^2+4xy^4-3y^2z):(-2xy^2)

Degree: 2

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

Dividing polynomial

100

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

16x^4y^3 : 8x^3y^2

2xy

200

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

56x^(3n)y^3 : 14x^(n+2)y

4x^(2n+2)y^2

300

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

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

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

400

Find the condition of n such that A is divisible by B.

A=7x^(n-1)y^5-5x^3y^4

B=5x^2y^n

n\in{3,4}

500

Find the condition of n such that A is divisible by B.

4x^ny^(n+1) : 3x^4y^6

n>=5 and n\in N