Factor
\frac{\left(x+2\right)\left(x+6\right)}{4}
Evaluate
\frac{\left(x+2\right)\left(x+6\right)}{4}
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\frac{x^{2}+8x+12}{4}
Factor out \frac{1}{4}.
a+b=8 ab=1\times 12=12
Consider x^{2}+8x+12. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+12. To find a and b, set up a system to be solved.
1,12 2,6 3,4
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 12.
1+12=13 2+6=8 3+4=7
Calculate the sum for each pair.
a=2 b=6
The solution is the pair that gives sum 8.
\left(x^{2}+2x\right)+\left(6x+12\right)
Rewrite x^{2}+8x+12 as \left(x^{2}+2x\right)+\left(6x+12\right).
x\left(x+2\right)+6\left(x+2\right)
Factor out x in the first and 6 in the second group.
\left(x+2\right)\left(x+6\right)
Factor out common term x+2 by using distributive property.
\frac{\left(x+2\right)\left(x+6\right)}{4}
Rewrite the complete factored expression.
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
Arithmetic
699 * 533
Matrix
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}