Laws of Exponents & Operations with Polynomials

Adding Polynomials

100

Add the following polynomials:

(x²+2x-4) + (-3x+2)

x²-x-2

200

Add the following polynomials:

(x²+2x) + (2x²+3x +3)

3x² +5x +3

300

Add the following polynomials:

(3x³-x²+1) + (x³+2x²-4)

4x³+x²-3

400

Add the following polynomials:

(2x³+4x+5) + (x²+2x-4)

2x³+x²+6x+1

500

Add the following polynomials:

(x²-3x+4) + (-3x²-2x-4)

-2x²-5x

Subtracting Polynomials

100

Subtract the following polynomials:

(x²+2x-4) - (-3x+2)

x² +5x -6

200

Subtract the following polynomials:

(x²+2x) - (2x²+3x +3)

-x² -x -3

300

Subtract the following polynomials:

(3x³-x²+1) - (x³+2x²-4)

2x³ -3x² +5

400

Subtract the following polynomials:

(2x³+4x+5) - (x²+2x-4)

2x³ -x² +2x +9

500

Subtract the following polynomials:

(x²-3x+4) - (-3x²-2x-4)

4x² -x +8

Multiplying Polynomials

100

Multiply the following polynomials: 

(x+5)(x-5)

x² -25

200

Multiply the following polynomials: 

(2x+2)(x+3)

2x² +8x +6

300

Multiply the following polynomials: 

(x+3)²

x²+6x+9

400

Multiply the following polynomials: 

(x-3)(x² +3x +3)

x³ -6x -9

500

Multiply the following polynomials: 

(x+2)(-x² -2x +1)

-x³ -4x² -3x +2

Dividing Polynomials

100

Dividing the polynomials. 

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

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

200

Divide the polynomial:

(34m³n² – 51m²n³) ÷ 17mn

2m²n – 3mn²

300

Divide. Write your answer in the form Q+ R/D

(12x3 + 15x2 + 11x + 17) / (x + 1)

12x2 + 3x + 8 + 9/(x + 1)

400

Divide. Write your answer in the form Q+ R/D

(2x^3 - 9x + 5) / (x - 2)

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

500

Divide. Write your answer in the form Q+ R/D

(2x^3+x^2-3x-2)/(x+1)

2x^2-x-2

Vocabulary

100

What is a coefficient?

The number in front of the variable

200

In a polynomial, every term must have an exponent that is a ________.

Non-negative integer

300

Some polynomials are named according to the number of terms. What is the name of polynomials with one term, two term, and three terms 

monomial, binomial, trinomial

400

What determines the degree of a polynomial?

The greatest exponent in the polynomial

500

All polynomials are closed under what operations?

Addition, Subtraction, and Multiplication

Laws of Exponents

100

Simplify the following and write your answer using only positive exponents

x^4* x^(-7)

1/x^3

200

Simplify the following. Write your answer using only positive exponents.

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

xy^2

300

Simplify the following. Write your answer using only positive exponents. 

(4x^2yz^3)^2

16x^4y^2z^6

400

Simplify the following. Write your answer using only negative exponents. 

(x^4 \cdot x^10)/x^-2

1/x^4

500

Simplify the following. Write your answer using only positive exponents. 

((-6^2 a^3 b)/(b^2))^-1

- b/(36 a^3 

Grade A Student

100

Determine Kelsey's error and correct it:

4x² + 5x² = 9x⁴

Kelsey incorrectly added the exponents. The correction should be:

4x² + 5x² = 9x²

200

Determine Enrique's mistake and correct it: 

4x³ + 5x³ + x²= 20x³ + x²

Enrique multiplied the coefficients instead of adding them. It should be:

4x³ + 5x³ + x²= 9x³ + x²

300

Determine Jose's error and correct it:

4x - (3x -2) = 4x - 3x -2 = x-2

Jose forgot to distribute the negative to the -2. It should be: 

4x - (3x -2) = 4x - 3x +2 = x +2 

400

Determine Irene's mistake and correct it:

2x(x-4) = 3x²-6x

Irene is adding the coefficients inserted of multiplying them. It should be:

2x(x-4) = 2x²-8x

500

Determine Rocio's mistake and correct it:

(x+3)² = x² + 9

Rocio squared each term instead of squaring the whole polynomial. It should be: 

(x+3)² = (x+3)(x+3) = x²+3x+3x+ 9 = x² +6x +9