Factor
\frac{\left(x-4\right)\left(7x-4\right)}{16}
Evaluate
\frac{7x^{2}}{16}-2x+1
Graph
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\frac{7x^{2}-32x+16}{16}
Factor out \frac{1}{16}.
a+b=-32 ab=7\times 16=112
Consider 7x^{2}-32x+16. Factor the expression by grouping. First, the expression needs to be rewritten as 7x^{2}+ax+bx+16. To find a and b, set up a system to be solved.
-1,-112 -2,-56 -4,-28 -7,-16 -8,-14
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 112.
-1-112=-113 -2-56=-58 -4-28=-32 -7-16=-23 -8-14=-22
Calculate the sum for each pair.
a=-28 b=-4
The solution is the pair that gives sum -32.
\left(7x^{2}-28x\right)+\left(-4x+16\right)
Rewrite 7x^{2}-32x+16 as \left(7x^{2}-28x\right)+\left(-4x+16\right).
7x\left(x-4\right)-4\left(x-4\right)
Factor out 7x in the first and -4 in the second group.
\left(x-4\right)\left(7x-4\right)
Factor out common term x-4 by using distributive property.
\frac{\left(x-4\right)\left(7x-4\right)}{16}
Rewrite the complete factored expression.
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