The area of a rectangle is given by the product of its length and width. Given the length and area of the rectangle, we can find the width by dividing the area by the length:
Width = Area / Length
So in this case, the width will be:
Width = (6x^4 - 8x^3 + 9x^2 - 3x - 12) / (3x - 4)
Now we need to simplify the expression. To do this, we will perform polynomial long division:
2x^3 + x^2 - 3x + 1
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3x - 4 | 6x^4 - 8x^3 + 9x^2 - 3x - 12
- 6x^4 + 8x^3
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x^3 + 9x^2
- x^3 + 4/3x^2
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7/3x^2 - 3x
- 7/3x^2 + 28/3x
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- 25/3x - 12
25/3x + 100/3
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- 136/3
The quotient is 2x^3 + x^2 - 3x + 1 and remainder is -136/3. Since the remainder is non-zero, the width cannot be expressed as a polynomial. The most simplified form of the width is:
Width = (6x^4 - 8x^3 + 9x^2 - 3x - 12) / (3x - 4).
Length is 3x - 4, area is 6x^4-8x^3+9x^2-3x-12
Express the width algebraically. Simplify answer completely
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