Factor
\left(x-3\right)\left(x^{2}+3x+8\right)
Evaluate
x^{3}-x-24
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x^{3}-x-24
Multiply and combine like terms.
\left(x-3\right)\left(x^{2}+3x+8\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -24 and q divides the leading coefficient 1. One such root is 3. Factor the polynomial by dividing it by x-3. Polynomial x^{2}+3x+8 is not factored since it does not have any rational roots.
x^{3}-24-x
Add -27 and 3 to get -24.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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