Laws of Exponents, and Multiplication and Division of Polynomials

LAW OF EXPONENT

10

(567)⁰

1

15

5^-2

1 / 25

30

Enumerate 4 laws on exponents.

Product of Power Rule

Quotient of Power Rule

Power of a Power Rule

Power of a Quotient Rule

Power of a Product Rule

Zero power Rule

Negative exponent Rule

40

(x+1)^-2(2x)

2x / (x + 1)²

50

( 7⁴ •7³)/(7³)²

7

MULTIPLYING POLYNOMIALS

10

x³•x²

x⁵

15

1 x (2x³+3x²+5x+7)

2x³+3x²+5x+7

30

(2x + 5)(2x – 5)

4x² - 25

40

(3r³ - r² )(r  + 5)

3r⁴ + 4r³ - 5r²

50

(x²+2x+1)(2x+1)

2x³ +5x² + 4x + 1

LONG DIVISION

10

4z² + z - 3 / z + 1

4z - 3

15

(x²-9) / (x+3)

x-3

30

(12x³+12x²+3x) / (6x+3)

2x² + x

40

(3x+2)² / 2

9x²  + 12x + 4 / 2 

50

(3x²+2x+2) / x-1, 

Find the remainder.

10

SYNTHETIC DIVISION

10

 -2/3mn^5-5/7m^5n^8

-mn^5(2/3-5/7m^4n^3)

15

6x² + 7x - 20 / 2x + 5

3x - 4

30

2y² - 5y -3 / y - 3

2y + 1

40

(6p³ + 7p² + 12p + 5) / (2p + 1)

3p² + 2p + 5

50

x² - x + 1 / x + 1,

 solve for the quotient and find its remainder.

Q= x + 1

R= 3