Exponent Rules and Polynomial Division

Synthetic Division

100

(6x³ + 3x² -12x -9) / (x+3)

6x² - 15x +33 + (108/x+3)

200

(4x³ -3x² + 2x +1) / (x-4)

4x² -19x +78 - (311/x-4)

300

(n² + 10n + 18) / (n +5)

n + 5 - (7/n +5)

400

(3x³ - 2x² - 150) / (x-4)

3x + 10 - (110/x-4)

500

(3x³ + 5x + 1) / (x+1)

3x² -3x + 8 - (7/x+1)

Long Division

100

(x² + 5x + 4) / (x+4)

x + 1

200

(3x³ - 2x² +7x - 4) / (x² -1)

3x - 2 + (4x-2/x² -1)

300

(3x³ + 4x + 11) / (x² - 3x +2)

(3x + 9) + (25x -7/x² - 3x +2)

400

(12x³ -11x² 9x + 18) / (4x+3)

3x² - 5x + 6

500

(x³ - 4x² + 2x + 5) / (x-2)

x² - 2x - 2 + (1/x-2)

Product/Quotient Rule

100

What is the product rule?

multiply the bases and add the exponents 

200

What is the Quotient Rule?

divide the bases and subtract the exponents 

300

x³ * x⁸

x¹¹

400

(x²y)(x³y⁴)

x⁵y⁵

500

(x²y⁵) / (xy³)

xy²

Zero Exponent/Power Rule

100

What is the zero exponent rule?

Any base raised to the zero exponent is equal to 1

200

What is he power rule?

write the base and multiply the exponents

300

x⁰

1

400

(7a³b^-1)

1

500

(z⁵)²

z¹⁰

Inverse

100

what is the inverse of f(x)=3x+2

x-2 / 3