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the area of a rectangular box is 24x³-76x²-28x square units. The width of this box is (12x²+4x) units. Write and simplify an expression for the length of the rectangle. (Please show steps:) NEED ASAP

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Banabanana

Answer:

(2x-7) units

Step-by-step explanation:

[tex]\tt length=\cfrac{area}{width}\\\\\\ length=\cfrac{24x^3-76x^2-28x}{12x^2+4x}=\cfrac{4x(6x^2-19x-7)}{4x(3x+1)}=\\\\\\=\cfrac{6x^2+2x-21x-7}{3x+1}=\cfrac{2x(3x+1)-7(3x+1)}{3x+1}=\\\\\\=\cfrac{(3x+1)(2x-7)}{3x+1}=2x-7[/tex]

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