Factor
\frac{\left(3x+2\right)\left(8x+3\right)}{6}
Evaluate
4x^{2}+\frac{25x}{6}+1
Graph
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\frac{24x^{2}+25x+6}{6}
Factor out \frac{1}{6}.
a+b=25 ab=24\times 6=144
Consider 24x^{2}+25x+6. Factor the expression by grouping. First, the expression needs to be rewritten as 24x^{2}+ax+bx+6. To find a and b, set up a system to be solved.
1,144 2,72 3,48 4,36 6,24 8,18 9,16 12,12
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 144.
1+144=145 2+72=74 3+48=51 4+36=40 6+24=30 8+18=26 9+16=25 12+12=24
Calculate the sum for each pair.
a=9 b=16
The solution is the pair that gives sum 25.
\left(24x^{2}+9x\right)+\left(16x+6\right)
Rewrite 24x^{2}+25x+6 as \left(24x^{2}+9x\right)+\left(16x+6\right).
3x\left(8x+3\right)+2\left(8x+3\right)
Factor out 3x in the first and 2 in the second group.
\left(8x+3\right)\left(3x+2\right)
Factor out common term 8x+3 by using distributive property.
\frac{\left(8x+3\right)\left(3x+2\right)}{6}
Rewrite the complete factored expression.
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Limits
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