Factor
\frac{\left(2x+3\right)\left(4x+1\right)}{4}
Evaluate
2x^{2}+\frac{7x}{2}+\frac{3}{4}
Graph
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\frac{8x^{2}+14x+3}{4}
Factor out \frac{1}{4}.
a+b=14 ab=8\times 3=24
Consider 8x^{2}+14x+3. Factor the expression by grouping. First, the expression needs to be rewritten as 8x^{2}+ax+bx+3. To find a and b, set up a system to be solved.
1,24 2,12 3,8 4,6
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 24.
1+24=25 2+12=14 3+8=11 4+6=10
Calculate the sum for each pair.
a=2 b=12
The solution is the pair that gives sum 14.
\left(8x^{2}+2x\right)+\left(12x+3\right)
Rewrite 8x^{2}+14x+3 as \left(8x^{2}+2x\right)+\left(12x+3\right).
2x\left(4x+1\right)+3\left(4x+1\right)
Factor out 2x in the first and 3 in the second group.
\left(4x+1\right)\left(2x+3\right)
Factor out common term 4x+1 by using distributive property.
\frac{\left(4x+1\right)\left(2x+3\right)}{4}
Rewrite the complete factored expression.
Examples
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{ 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}