Question 1034651
The area of a rectangular field is 2c³-c²+6 square units. 
If the length of the field is c−2 units, what is its width?
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First let's do this simpler one:
</pre>
The area of a rectangular field is 5 square units. 
If the length of the field is 3 units, what is its width?
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A = LW

Substitute 5 for A and 3 for L:

5 = 3W

Divide both sides by 3

{{{5/3}}}{{{""=""}}}{{{3W/3}}}

{{{5/3}}}{{{""=""}}}{{{cross(3)W/cross(3)}}}

 <u> 1</u>
3)5
  <u>3</u>
  2
Answer: The width is {{{1&2/3}}} 

Now let's do yours exactly the same way:
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The area of a rectangular field is 2c³-c²+6 square units. 
If the length of the field is c&#8722;2 units, what is its width?
<pre>
A = LW

Substitute 2c³-c²+6 for A and c-2 for L:

2c³-c²+6 = (c-2)W

Divide both sides by (c-2)

{{{(2c^3-c^2+6)/(c-2)}}}{{{""=""}}}{{{(c-2)W/(c-2)}}}

{{{(2c^3-c^2+6)/(c-2)}}}{{{""=""}}}{{{cross(c-2)W/cross(c-2)}}}

   <u>      2c² + 3c + 6</u>
c-2)2c³ - c² + 0c + 6
    <u>2c³ -4c²</u>
         3c² + 0c
         <u>3c² - 6c</u>
               6c + 6
               <u>6c -12</u>
                   18
  

Answer: The width is {{{2c^2 + 3c + 6 + 18/(c-2)}}} 

Edwin</pre>