Factor
2x\left(2x-3\right)\left(4x^{2}+6x+9\right)
Evaluate
16x^{4}-54x
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2\left(8x^{4}-27x\right)
Factor out 2.
x\left(8x^{3}-27\right)
Consider 8x^{4}-27x. Factor out x.
\left(2x-3\right)\left(4x^{2}+6x+9\right)
Consider 8x^{3}-27. Rewrite 8x^{3}-27 as \left(2x\right)^{3}-3^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).
2x\left(2x-3\right)\left(4x^{2}+6x+9\right)
Rewrite the complete factored expression. Polynomial 4x^{2}+6x+9 is not factored since it does not have any rational roots.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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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
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}