🤩 Unit 8 - Exponent Rules & Polynomial Operations 😛

Exponents Rules

100

Solve and answer the question:

2686317884⁰

What does it mean when the exponent is zero?

1

The answer will always be 1.

200

Solve and answer the question:

6^-3

What do you do when the exponent is negative?

1/216

You put the term (6^-3) under 1, making it a fraction. Then turn the exponent into a positive number (6³) and solve. 1/6³ 

300

Solve and answer the question:

14³ * 14²

What do you do when you have to multiply two numbers with the same base/integer?

14⁵ (537824)

You add the exponents.

400

Solve and answer the question:

32⁸⁵ / 32⁷⁹

What do you do when you have to divide two numbers with the same base/integer?

32⁶ (1073741824)

You subtract the exponents.

500

Solve and answer the question:

4^3/2

√4³
= +-8

Subtract Polynomials

100

(2x - 7) - (3x² - 23x + 4)

hint - When subtracting polynomials, flip the symbols. (+ and -) For example: x - (-2x + 4) is equal to x + 2x - 4

-2x² +25x -11

200

A= 6x² - 2x + 9 

B= -3x² + 5x - 3

Solve A - B

hint - When subtracting polynomials, flip the symbols. (+ and -) For example: x - (-2x + 4) is equal to x + 2x - 4

9x² - 7x + 12

300

Subtract (11b² - 4b + 7) from (b² + 8b -9)

hint - When subtracting polynomials, flip the symbols. (+ and -) For example: x - (-2x + 4) is equal to x + 2x - 4

-10b² + 12b - 16

400

(12x² + 3xy - 5y²) - (8x² + 3xy + 4y²)

hint - When subtracting polynomials, flip the symbols. (+ and -) For example: x - (-2x + 4) is equal to x + 2x - 4

4x² - 9y²

500

(-x² + 2xy + 8y²) - (15x² + 3xy - 7y²)

hint - When subtracting polynomials, flip the symbols. (+ and -) For example: x - (-2x + 4) is equal to x + 2x - 4

-16x² - 1xy + 15y²

Add Polynomials

100

(3x + 5) + (2x + 7)

5x + 12

200

(4x² + 3x + 1) + (2x² + 5x +6)

6x² + 8x + 7

300

(5x³ + 2x² - 4x + 8) + (3x³ - x² + 6x - 5)

8x³ + x² + 2x + 3

400

(7x⁴ - 3x³ + 2x² - x + 4) + (-2x⁴ + 5x³ - x² + 3x - 6)

tip - write it out first

5x⁴ + 2x³ + x² + 2x - 2

500

(4x⁵ + 3x⁴ - 2x³ + x² - 5x + 7) + (2x⁵ - x⁴ + 4x³ - 3x² + 6x - 9)

tip - take your time and write it out; it's easier than you think

6x⁵ + 2x⁴ + 2x³ - 2x² + x - 2

Multiply Polynomials

100

3x(2x+5)

6x² + 15x

200

(x+3)(x-2)

x² + x - 6

300

(2x + 1)(x² - 3x + 4)

2x³ - 5x² + 5x + 4

400

(x² + 2x + 1)(x² - x + 3)

x⁴ + x³ + 2x² + 5x + 3

500

(2x² + 3x - 4)(x² - 2x + 5)

2x⁴ - x³ + 23x - 20

Divide Polynomials by Monomials

100

(6x² + 12x) / 3x

2x + 4

200

(10³ - 5x² + 15x) / 5x

2x² - x + 3

300

(8x⁴ - 4x³ + 12x - 16) / 4x

2x³ - x² + 3 - 4/x

400

(12x³y² - 6x²y + 18xy³) / 6xy

2x²y - x + 3y²

500

(20x⁴y³ - 15x³y² + 30x²y - 5xy⁴) / 5xy

tip - take your time and write it out

4x³y² - 3x²y + 6x - y³