Adding, Subtracting, Multiplying, and Dividing 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+1) + (x³+2x²)

1 + 4x³+2x² 

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(x² - 3x +3) + 9

-x³ + 3x² -3x +9

500

Multiply the following polynomials: 

(x+2)(-x² -2x +1)

-x³ -4x² -3x +2

Vocabulary

100

For -3x, what is the coefficient?

-3

200

How many terms does  (2 + 3x + 4y)  have?

3

300

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

monomial, binomial, trinomial

400

What determines the degree of a polynomial?

The greatest exponent in the polynomial

500

For polynomial  3x³ - 4y + 8t - x

The number of terms=? The variables are ? The coeficients are ?

4 terms; x, y, and t; 3, -4, 8, and -1

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