Factor
\frac{4\left(2x-1\right)\left(4x^{2}+2x-7\right)}{17}
Evaluate
\frac{32x^{3}-64x+28}{17}
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\frac{4\left(8x^{3}-16x+7\right)}{17}
Factor out \frac{4}{17}.
\left(2x-1\right)\left(4x^{2}+2x-7\right)
Consider 8x^{3}-16x+7. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 7 and q divides the leading coefficient 8. One such root is \frac{1}{2}. Factor the polynomial by dividing it by 2x-1.
\frac{4\left(2x-1\right)\left(4x^{2}+2x-7\right)}{17}
Rewrite the complete factored expression. Polynomial 4x^{2}+2x-7 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
Linear equation
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
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