Factor
4x\left(x-3\right)\left(x+3\right)\left(3-x^{2}\right)
Evaluate
-4x^{5}+48x^{3}-108x
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4\left(-x^{5}+12x^{3}-27x\right)
Factor out 4.
x\left(-x^{4}+12x^{2}-27\right)
Consider -x^{5}+12x^{3}-27x. Factor out x.
\left(x^{2}-9\right)\left(-x^{2}+3\right)
Consider -x^{4}+12x^{2}-27. Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -x^{4} and n divides the constant factor -27. One such factor is x^{2}-9. Factor the polynomial by dividing it by this factor.
\left(x-3\right)\left(x+3\right)
Consider x^{2}-9. Rewrite x^{2}-9 as x^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
4x\left(x-3\right)\left(x+3\right)\left(-x^{2}+3\right)
Rewrite the complete factored expression. Polynomial -x^{2}+3 is not factored since it does not have any rational roots.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}