Answer:
Step-by-step explanation:
Area of a rectangle is found by multiplying length times width. We are given the area and the length, and need to solve for width. The equation to begin this process is
[tex]m^2+2m-80=(m+10)width[/tex]
To solve for the width, we divide the m+10 away, giving us:
[tex]\frac{m^2+2m-80}{m+10}=width[/tex]
Use synthetic division for this, with a value of -10:
-10 | 1 2 -80
Bring down the 1 and multiply it by -10, and put that product up under the 2:
-10 | 1 2 -80
-10
----------------------
1
Now add 2 and -10 and multiply that sum by -10 and put it up under the -80
-10 | 1 2 -80
-10 80
------------------------
1 -8 0
The remainder is 0, so the depressed polynomial is 1m - 8. That is the factor that represents the width of the rectangle. You could have also done long division of polynomials, but that is much to difficult to type out.
