Operations on Polynomials

Adding and Subtracting

100

Subtract the following polynomials:

(x²+2x-4) - (-3x+2)

x² +5x -6

200

Add the following polynomials:

(x²+2x) + (2x²+3x +3)

3x² +5x +3

300

Subtract the following polynomials:

(3x³-x²+1) - (x³+2x²-4)

2x³ -3x² +5

400

Add the following polynomials:

(2x³+4x+5) + (x²+2x-4)

2x³+x²+6x+1

500

Subtract the following polynomials:

(2x³+4x+5) - (x²+2x-4)

2x³ -x² +2x +9

Multiplying and Special Products

100

Multiply the following polynomials: 

(x+3)²

x²+6x+9

200

Multiply the following polynomials: 

(2x+2)²

4x² +8x +4

300

Find the area with a width w and length 2w + 2.

Area is 2w² + 2w units².

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

Divide the polynomial:

(m² – 2mn) ÷ m

m – 2n

200

Divide the polynomial:

(18r⁵ + 36r⁴ + 27r³ ) ÷ 9r

2r4 + 4r3 + 3r2

300

Divide the polynomial:

(34m³n² – 51m²n³) ÷ 17mn

2m²n – 3mn²

400

56x³y³  divided by 14x²y⁵

4x/y²

500

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

(−12x⁴y + 4x³ − 8x²y²) / (−4x²)

3x²y - x + 2y²

Vocabulary

100

What is a coefficient?

The number in front of the variable

200

When multiplying polynomials, we ________ their exponents. 

add

300

Write the following in standard form:

12x - 18 - 5x² + 17x⁴

Determine its degree.

Standard form: 17x⁴ - 5x² + 12x - 18 

degree: 4 (Quartic)

400

What determines the degree of a polynomial?

sum of all term's exponents

500

Any number or expression raised to the power zero is always equal to ________. 

1

Error Analysis

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