Adding, Subtracting, and Multiplying 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

Find the perimeter of a square with a side length of (3x² - 2x + 1).

12x² - 8x + 4

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

The perimeter of a triangle is 16x + 4. Two sides of the triangle are (8x + 7) and (3x + 2). 

Find the expression for the 3rd side of the triangle.

5x - 5

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

Find the area of a rectangle with a length of (2x - 1) and a width of (7x - 1).

14x² - 9x + 1

Vocabulary

100

What is a coefficient?

The number in front of the variable

200

How do you write a polynomial in standard?

Arrange each term from greatest exponent to smallest exponent

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

What is the degree of a quadratic polynomial?

2

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)(x+3) = x² + 9

Rocio only distributed and multiplied twice, when he should have distributed and multiplied 4 times. It should be: 

(x+3)(x+3) = x²+3x+3x+ 9 = x² +6x +9