# Chapter 4

- StudyBlue
- Wisconsin
- University of Wisconsin - Madison
- Mathematics
- Mathematics 091
- Harrison
- Chapter 4

**Created:**2011-03-25

**Last Modified:**2011-05-26

x

^{4}*x

^{3}= x

^{4+.3}= x

^{7}

**and subtract the exponents in the denominator from the exponents in the numerator.**

__keep the base__x

^{5}/x

^{3}= x*x*x*x*x*/x*x*x* = 1x

^{2}/1 = x

^{2}

Pg 234a

3

^{0}= 1

x

^{0}= 1

(x

^{3})

^{2}= x

^{3*2}= x

^{5}

(ax/by)

^{2}= a

^{2}x

^{2}/b

^{2}y

^{2}

x

^{-2}= 1/x

^{2}

Multiply the number obtained in step 1 by 10 raised to the count(power) .

18,500 = 1.85*10

^{4}

If the exponent is negative, move the decimal point in the number to the left.

If the exponent is 0, do not move the decimal point. Drop the factor 10

^{0}since it equals 1. This will result in a number greater than or equal to 1 but less than 10.

8.3x10

^{4}- 1.02x10

^{5}= 8.3x10

^{4}-10.2x10

^{4}

^{n}, for any real number a and any

__n.__

**whole number**Examples: 8x, 1/3x-4, x

^{2}-2x+1

Not Polynomial: 4x

^{1/2}, 3x

^{2}+4x

^{-1}+5, (neg exponent) 4+1/x (1/x=x

^{-1}, negative exponent)

Binomial : two-termed polynomial

Trinomial: three-termed polynomial

4x

^{2}Second

2y

^{5}Fifth

-5x First

3 Zero

8x

^{3}+2x

^{2}-3x+4 Third (8x

^{3}is the highest-degree term)

x

^{2}-4 Second (x

^{2}is highest-degree term)

6x-5 First (6x 6x

^{1 }is the highest degree-term)

4 Zero

x

^{2}y

^{4}+2x+3 Sixth (x

^{2}y

^{4}is the highest-degree term)

2) Add the terms in each column.

pg 263

__term within the parentheses of the polynomial__

**every**__.)__

**being subtracted**2) Combine like terms

2) Change the sign of each term in the polynomial being subtracted. (This step can be done mentally, if you like)

3) Add the terms in each column.

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