Factor
\frac{\left(2x-5\right)\left(4x^{2}+\frac{15x}{2}-5\right)}{10}
Evaluate
\frac{4x^{3}}{5}-\frac{x^{2}}{2}-\frac{19x}{4}+\frac{5}{2}
Graph
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\frac{16x^{3}-10x^{2}-95x+50}{20}
Factor out \frac{1}{20}.
\left(2x-5\right)\left(8x^{2}+15x-10\right)
Consider 16x^{3}-10x^{2}-95x+50. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 50 and q divides the leading coefficient 16. One such root is \frac{5}{2}. Factor the polynomial by dividing it by 2x-5.
\frac{\left(2x-5\right)\left(8x^{2}+15x-10\right)}{20}
Rewrite the complete factored expression. Polynomial 8x^{2}+15x-10 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}