One dimension of a cube is increased by 1 inch to form a rectangular block. Suppose that the volume of the new block is 150 cubic inches. Find the length of an edge of the original cube.
Solution:
Let x be the length of the side the original cube.
x+1 be the length of one dimension of the rectangular box.
Recall that the volume of a rectangular box is lwh (V=lwh)
150 = lwh
150 = (x)(x)(x+1)
150 = x^3 + x^2
x^3 + x^2 - 150 = 0
Using Factor Theorem, look for the possible roots of the given polynomial equation. in this case, choose x=5 and use synthetic division
1 1 0 -150 |_ 5
5 30 150
1 6 30 0 ---> 0 remainder
Then, 5 is one of the roots.
Therefore, the length of an edge of the original cube is 5 inches.
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