Factor
3x\left(4x-3\right)\left(5x^{2}+1\right)
Evaluate
3x\left(4x-3\right)\left(5x^{2}+1\right)
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3\left(20x^{4}-15x^{3}+4x^{2}-3x\right)
Factor out 3.
x\left(20x^{3}-15x^{2}+4x-3\right)
Consider 20x^{4}-15x^{3}+4x^{2}-3x. Factor out x.
\left(4x-3\right)\left(5x^{2}+1\right)
Consider 20x^{3}-15x^{2}+4x-3. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -3 and q divides the leading coefficient 20. One such root is \frac{3}{4}. Factor the polynomial by dividing it by 4x-3.
3x\left(4x-3\right)\left(5x^{2}+1\right)
Rewrite the complete factored expression. Polynomial 5x^{2}+1 is not factored since it does not have any rational roots.
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{ x } ^ { 2 } - 4 x - 5 = 0
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\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]
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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