Factor
\frac{\left(4x-3\right)\left(4x-1\right)}{16}
Evaluate
x^{2}-x+\frac{3}{16}
Graph
Share
Copied to clipboard
\frac{16x^{2}-16x+3}{16}
Factor out \frac{1}{16}.
a+b=-16 ab=16\times 3=48
Consider 16x^{2}-16x+3. Factor the expression by grouping. First, the expression needs to be rewritten as 16x^{2}+ax+bx+3. To find a and b, set up a system to be solved.
-1,-48 -2,-24 -3,-16 -4,-12 -6,-8
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 48.
-1-48=-49 -2-24=-26 -3-16=-19 -4-12=-16 -6-8=-14
Calculate the sum for each pair.
a=-12 b=-4
The solution is the pair that gives sum -16.
\left(16x^{2}-12x\right)+\left(-4x+3\right)
Rewrite 16x^{2}-16x+3 as \left(16x^{2}-12x\right)+\left(-4x+3\right).
4x\left(4x-3\right)-\left(4x-3\right)
Factor out 4x in the first and -1 in the second group.
\left(4x-3\right)\left(4x-1\right)
Factor out common term 4x-3 by using distributive property.
\frac{\left(4x-3\right)\left(4x-1\right)}{16}
Rewrite the complete factored expression.
Examples
Quadratic equation
{ 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}