Factor
y\left(x+5\right)\left(6x+1\right)
Evaluate
y\left(x+5\right)\left(6x+1\right)
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y\left(6x^{2}+31x+5\right)
Factor out y.
a+b=31 ab=6\times 5=30
Consider 6x^{2}+31x+5. Factor the expression by grouping. First, the expression needs to be rewritten as 6x^{2}+ax+bx+5. To find a and b, set up a system to be solved.
1,30 2,15 3,10 5,6
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 30.
1+30=31 2+15=17 3+10=13 5+6=11
Calculate the sum for each pair.
a=1 b=30
The solution is the pair that gives sum 31.
\left(6x^{2}+x\right)+\left(30x+5\right)
Rewrite 6x^{2}+31x+5 as \left(6x^{2}+x\right)+\left(30x+5\right).
x\left(6x+1\right)+5\left(6x+1\right)
Factor out x in the first and 5 in the second group.
\left(6x+1\right)\left(x+5\right)
Factor out common term 6x+1 by using distributive property.
y\left(6x+1\right)\left(x+5\right)
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}