Factor
\frac{\left(2x+7\right)\left(4x+1\right)}{8}
Evaluate
x^{2}+\frac{15x}{4}+\frac{7}{8}
Graph
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\frac{8x^{2}+30x+7}{8}
Factor out \frac{1}{8}.
a+b=30 ab=8\times 7=56
Consider 8x^{2}+30x+7. Factor the expression by grouping. First, the expression needs to be rewritten as 8x^{2}+ax+bx+7. To find a and b, set up a system to be solved.
1,56 2,28 4,14 7,8
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 56.
1+56=57 2+28=30 4+14=18 7+8=15
Calculate the sum for each pair.
a=2 b=28
The solution is the pair that gives sum 30.
\left(8x^{2}+2x\right)+\left(28x+7\right)
Rewrite 8x^{2}+30x+7 as \left(8x^{2}+2x\right)+\left(28x+7\right).
2x\left(4x+1\right)+7\left(4x+1\right)
Factor out 2x in the first and 7 in the second group.
\left(4x+1\right)\left(2x+7\right)
Factor out common term 4x+1 by using distributive property.
\frac{\left(4x+1\right)\left(2x+7\right)}{8}
Rewrite the complete factored expression.
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Limits
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