Factor
\frac{x\left(3-x\right)\left(x-8\right)}{4}
Evaluate
\frac{x\left(3-x\right)\left(x-8\right)}{4}
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\frac{-x^{3}+11x^{2}-24x}{4}
Factor out \frac{1}{4}.
x\left(-x^{2}+11x-24\right)
Consider -x^{3}+11x^{2}-24x. Factor out x.
a+b=11 ab=-\left(-24\right)=24
Consider -x^{2}+11x-24. Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx-24. To find a and b, set up a system to be solved.
1,24 2,12 3,8 4,6
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 24.
1+24=25 2+12=14 3+8=11 4+6=10
Calculate the sum for each pair.
a=8 b=3
The solution is the pair that gives sum 11.
\left(-x^{2}+8x\right)+\left(3x-24\right)
Rewrite -x^{2}+11x-24 as \left(-x^{2}+8x\right)+\left(3x-24\right).
-x\left(x-8\right)+3\left(x-8\right)
Factor out -x in the first and 3 in the second group.
\left(x-8\right)\left(-x+3\right)
Factor out common term x-8 by using distributive property.
\frac{x\left(x-8\right)\left(-x+3\right)}{4}
Rewrite the complete factored expression.
Examples
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y = 3x + 4
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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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