Pre-Algebra Demystified

1. (x^2 þ3xþ2)(xþ1)


2. (3x^2 þ2xþ5)(x
   6)


3. (2x^2 þ4x
   1)(2x
   3)


4. (x^3
   2x^2 þ2xþ1)(x
   5)


5. (x^2 þ2xþ7)(x^2
   x
   6)

ANSWERS

1. x^3 þ4x^2 þ5xþ 2


2. 3x^3
   16x^2
   7x
   30


3. 4x^3 þ2x^2
   14xþ 3


4. x^4
   7x^3 þ12x^2
   9x
   5


5. x^4 þx^3
   x^2
   19x
   42

Division of Monomials

When one variable is divided by another variable with the same base, the
exponent of the variable in the denominator is subtracted from the exponent
of the variable in the numerator. For example,

x^6

x^2

¼

xxxxxx

xx

¼x^6 
^2 ¼x^4

In general,

xm

xn

¼xm
n

EXAMPLE

Divide x^5 by x^3.

SOLUTION

x^5

x^3

¼x^5 
^3 ¼x^2

To divide a monomial by a monomial, divide the numerical coefficients and

then subtract the exponents of the same variables.

EXAMPLE

Divide 15x^5 by
5x^3.

CHAPTER 12 Monomials and Polynomials 245