Polynomials

Adding Polynomials

100

Add the Polynomials

(4x + 9) +(x - 4)

5x + 5

200

Add the polynomials:

(-3a - 2) + (7a + 5)

4a + 3

300

Add the polynomials:

(x² +3x + 5) + ( -x² +6x)

9x + 5

400

Add the polynomials:

(t² + 3t³ -3) + (2t² +7t -2t³) 

t³ +3t² +7t -3

500

Add the polynomials 

(-14x⁴ + 5x² + 16) + (12x⁴ - 3x³ - 12)

-2x⁴ - 3x³ + 5x² + 4

600

Add the polynomials: 

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

Subtracting Polynomials

100

Subtract the polynomials:

(g - 4) - (3g - 6)

-2g + 2

200

Subtract the polynomials:

(-5h - 2) - (7h +6)

-12h - 8

300

Subtract the polynomials:

(-x² - 5) - (-3x² -x -8)

2x² + x +3

400

Subtract the Polynomials:

(k² + 6k³ -4) - (5k³ + 7k -3k²)

k³ + 4k² -7k -4

500

Subtract the Polynomials:

(2x - 3x) - (x² -2x + 4)

-x² + x - 4

600

Subtract the following polynomials

(3 - 6x⁵ - 8x⁴) - (-6x⁴ - 3x - 8x⁵)

2x⁵ - 2x⁴ + 3x + 3

Application Questions

100

Find the perimeter with a width w and length 2w + 2

Perimeter is 3w + 2 units

200

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

Area is 2w² + 2w units²

300

Find the perimeter of a rectangle with a width of 3wz - 3z and the length of 10z

Perimeter is 3wz + 7z units

400

Find the perimeter of a square whose side length is 5x + 5

20x + 20 units

500

What is the area of a square with a width of 

(3r+ 5)

9r² + 30r + 25

600

The length of a triangle is given as 3wz and the width is given as 10z. What is the area? 

30wz²

Multiplying Polynomials

100

Multiply the Polynomials:

3x² (2x⁴)

6x⁶

200

Multiply the Polynomials:

3x²(2x + 4x² - 5)

12x⁴ + 6x² - 15x²

300

Multiply the polynomials 

(4x² - 12)(2x + 5)

8x³ + 20x² - 24x - 60

400

Multiply the Polynomials:

(x-2)(x+6)

x²+4x-12

500

Multiply the Polynomials:

(3x-6)(5x+3)

15x²-21x-18

600

Multiply the Polynomials:

(x - 1)(−8x² − 6x − 12 )

-8x³ - 6x² - 12x + 8x² + 6x + 12

-8x³ + 2x² - 6x + 12 (Correct Answer)

Classifying and Properties

100

Which of these is in standard form? Why

1. x + 1

2. x³ - 4x + x²

3. 15x + 10x² - 5x⁴

1; order from least to greatest exponent

200

Write the following in standard form:

-8 - 11x + 3x⁴ + 12x²

What is the leading degree and the leading coefficient?

3x⁴ +12x² - 11x - 8

Leading degree: 4 

Leading coefficient: 3

300

Write the following in standard form:

12x - 18 - 5x² + 17x⁴

What is the leading degree and the leading coefficient?

Standard form: 17x⁴ - 5x² + 12x - 18 

Leading degree: 4 (Quartic)

Leading coefficient: 17

400

What is the degree of the following term?

-2x

Linear (1)

500

Put the polynomial in standard form. Classify the polynomial by degree & number of terms:

 - 3x - 4x² - 7

Standard form:  - 4x² - 3x - 7

Leading degree: 2 (quadratic polynomial) 

3 terms so it is a trinomial

600

State the degree and name for this polynomial:

3x⁴- 12x³

Quartic (4); Binomial

Exponent Rules

100

True or False

When multiplying monomials the coefficients and exponents are multiplied.

False

The coefficients are multiplied, but the exponents are added together.

200

Name the Rule and how it works

x^0

Zero Exponent Rule

The term equals to 1

300

Name the Rule and how it works

x^-1

Negative Exponent Rule

Converts term into a fraction, moves the variable to the denominator while changing the exponent to a positive.

400

Name the Rule and how it works

(x^a)/(x^b)

Quotient Rule

Subtracts Exponents

500

Name the Rule and how it works

(x^a)^b

Power Rule

Multiplies Exponents

600

Name the Rule and how it works

x^a*x^b

Product Rule

Adds exponents