Use the given volume of a box and its length and width to express the height of the box algebraically. (Simplify your answer completely.)
Volume is
10x^3 + 47x^2 + 16x − 48,
length is
5x − 4,
width is
2x + 3
+128407 V = L * W * H ...so...
10x^3 + 47x^2 + 16x - 48 = [ 5x - 4] [ 2x + 3] * H
10x^3 + 47x^2 + 16x - 48 = [ 10x^2 - 8x + 15x -12 ] * H
10x^3 + 47x^2 + 16x - 48 = [ 10x^2 + 7x -12 ] * H
We can find the height by dividing both sides by [10x^2 + 7x -12]
So
H = [10x^3 + 47x^2 + 16x -48] / [ 10x^2 + 7x - 12 ]
Performing ploynomial division to find the height , we have
x + 4
10x^2 + 7x - 12 [ 10x^3 + 47x^2 + 16x - 48 ]
10x^3 + 7x^2 -12x
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40x^2 + 28x - 48
40x^2 + 28x - 48
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So...the height = [ x + 4 ]
