SOLUTION: How do I find the width of the rectangle expressed algebraically with the given length and area? Length: 3x-4 Area: 6x^4-8x^3+9x^2-9x-4

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Question 1136873: How do I find the width of the rectangle expressed algebraically with the given length and area?
Length: 3x-4
Area: 6x^4-8x^3+9x^2-9x-4
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Length: 3x-4
Area: 6x%5E4-8x%5E3%2B9x%5E2-9x-4+
Area=Length%2AWidth
Width=Area%2FLength

so, you need to divide 6x%5E4-8x%5E3%2B9x%5E2-9x-4+by+3x-4 to find the width
%286x%5E4-8x%5E3%2B9x%5E2-9x-4%29%2F%283x-4%29....factor numerator completely
%286x%5E4-8x%5E3%2B9x%5E2-6x-3x-4%29%2F%283x-4%29.....write -9x as -12x%2B3x
%28%286x%5E4-8x%5E3%29%2B%289x%5E2-12x%29%2B%283x-4%29%29%2F%283x-4%29.......group
%282x%5E3%283x-4%29%2B3x%283x-3%29%2B%283x-4%29%29%2F%283x-4%29
%28%283+x+-+4%29+%282+x%5E3+%2B+3+x+%2B+1%29%29%2F%283x-4%29....simplify
2+x%5E3+%2B+3+x+%2B+1=> your answer for the width


Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
Area(A) of a rectangle is length * width
:
We are given the length and area, let w be the width
:
(3x-4) * w = 6x^4 -8x^3 +9x^2 -9x -4
:
w = (6x^4 -8x^3 +9x^2 -9x -4)/(3x-4) = 2x^3 +3x +1
:
This problem is solved by polynomial long division
: