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One obvious root of this is x = 1, so (x-1) is a factor.
Use long division of (x3 -1)/(x-1) and the quotient (x2 + x + 1) will be another factor.
So (x3 -1) = (x-1)(x2 + x + 1).
Remember that a cubic polynomial will always have 3 roots. It will either be 1 pure real root and 2 complex roots, or 3 pure real root. In this case (x2 + x + 1) has two complex roots, and cannot be factored with real numbers.
In general, any odd-powered polynomial (3rd order, 5th order etc), will have at least one pure real root, and then pairs of either pure-real or complex roots.
Any even powered polynomial (2nd order, 4th order, etc) will have pairs of either pure-real, or complex roots.
Don't be fooled if you only find one root. Example: (x2 + 2x + 1) actually has a double root, as it is factored into (x+1)(x+1).
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How do you factor x minus 1 cubed minus x plus 1 cubed?
(x - 1)(x - 1)(x - 1) - (x + 1)(x + 1)(x + 1)
How do you factor variable cubed minus the variable?
x(x + 1)(x -1)
How do you factor x cubed minus five x squared plus x minus 5?
(x - 5)(x^2 + 1)
How do you factor the expression x cubed minus x squared plus x minus 3?
x³ - x² + x - 3 (x² + 1)(x - 1) - 2
How do you factor X cubed minus 20x squared plus 19x?
x(x - 19)(x - 1)
How do you factor x minus 1 cubed minus x plus 1 cubed?
(x - 1)(x - 1)(x - 1) - (x + 1)(x + 1)(x + 1)
How do you factor variable cubed minus the variable?
x(x + 1)(x -1)
Factor x cubed minus one?
(x - 1)(x^2 + x + 1)
How do you factor the expression x cubed minus 1?
(x - 1)(x^2 + x + 1)
How do you factor x cubed minus 27?
t3-1/27
How do you factor x cubed minus x squared plus x?
Factor out the GCF and get X(X2-X+1).
How do you factor x cubed minus five x squared plus x minus 5?
(x - 5)(x^2 + 1)
What is x minus 1 cubed?
xcubed-1 Answer::(X-1)(Xsquared+X+1) when you factor xcubed minus a number its the same thing as x cubed minus y cubed and x cubed minus y cubed factors to:: (x-y)(xsquared+xy+y squared) the first factor, (x-y), is the cubed root of the first and the cubed root of the second, so in the answer i have (x-1), which is x cubed minus one cubed :) the second factor, (xsquared+xy+ysquared), you take the first number squared, Xsquared, then the first and second one multiplied together, XY, and then the second number squared, Ysquared, so in the answer i have (xsquared+x+1), which is x squared, then x times 1 which is just x, and positive 1, which is negative 1 squared :) x^3 - 1
How do you factor 9x cubed plus 18x squared minus x minus 2?
(x + 2)(3x - 1)(3x + 1)
How do you factor the expression x cubed minus x squared plus x minus 3?
x³ - x² + x - 3 (x² + 1)(x - 1) - 2
How do you factor X cubed minus 20x squared plus 19x?
x(x - 19)(x - 1)
How do you factor 64 x cubed minus y cubed?
64 x cubed minus y cubed is (4x - y)(16x^2 + 4xy + y^2)
