Factor
-\frac{\left(x-60\right)\left(x+4\right)}{8}
Evaluate
-\frac{\left(x-60\right)\left(x+4\right)}{8}
Graph
Share
Copied to clipboard
\frac{-x^{2}+56x+240}{8}
Factor out \frac{1}{8}.
a+b=56 ab=-240=-240
Consider -x^{2}+56x+240. Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx+240. To find a and b, set up a system to be solved.
-1,240 -2,120 -3,80 -4,60 -5,48 -6,40 -8,30 -10,24 -12,20 -15,16
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -240.
-1+240=239 -2+120=118 -3+80=77 -4+60=56 -5+48=43 -6+40=34 -8+30=22 -10+24=14 -12+20=8 -15+16=1
Calculate the sum for each pair.
a=60 b=-4
The solution is the pair that gives sum 56.
\left(-x^{2}+60x\right)+\left(-4x+240\right)
Rewrite -x^{2}+56x+240 as \left(-x^{2}+60x\right)+\left(-4x+240\right).
-x\left(x-60\right)-4\left(x-60\right)
Factor out -x in the first and -4 in the second group.
\left(x-60\right)\left(-x-4\right)
Factor out common term x-60 by using distributive property.
\frac{\left(x-60\right)\left(-x-4\right)}{8}
Rewrite the complete factored expression.
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}