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sqrt(x4) = x4/2 = x2
2 cubes wide x 3 cubes long x 4 cubes high. 2 X 3 X4 6 X 4 24 cubes
The answer to x4+x3-14x2+4x+6 divided by x-3 is x3+4x2-2x-2
x4 + 3x3 - x2 - 9x - 6 = 0 x4 + x3 + 2x3 + 2x2 - 3x2 - 3x - 6x - 6 = 0 x3(x + 1) + 2x2(x + 1) - 3x(x + 1) - 6(x + 1) = 0 (x + 1)(x3 + 2x2 - 3x - 6) = 0 (x + 1)[x2(x + 2) - 3(x + 2)] = 0 (x + 1)(x + 2)(x2 - 3) = 0 So x + 1 = 0 so that x = -1 or x + 2 = 0 so that x = -2 or x2 - 3 = 0 so that x = +/- sqrt(3)
x4 - x2 - 12 = (x2 + 3) (x2 - 4)And (x2 - 4) = (x + 2) (x - 2)So the original expression = (x2+ 3) (x + 2) (x - 2)