Factor
-\left(x-28\right)\left(x+1\right)
Evaluate
-\left(x-28\right)\left(x+1\right)
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-x^{2}+27x+28
Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
a+b=27 ab=-28=-28
Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx+28. To find a and b, set up a system to be solved.
-1,28 -2,14 -4,7
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -28.
-1+28=27 -2+14=12 -4+7=3
Calculate the sum for each pair.
a=28 b=-1
The solution is the pair that gives sum 27.
\left(-x^{2}+28x\right)+\left(-x+28\right)
Rewrite -x^{2}+27x+28 as \left(-x^{2}+28x\right)+\left(-x+28\right).
-x\left(x-28\right)-\left(x-28\right)
Factor out -x in the first and -1 in the second group.
\left(x-28\right)\left(-x-1\right)
Factor out common term x-28 by using distributive property.
-x^{2}+27x+28=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-27±\sqrt{27^{2}-4\left(-1\right)\times 28}}{2\left(-1\right)}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-27±\sqrt{729-4\left(-1\right)\times 28}}{2\left(-1\right)}
Square 27.
x=\frac{-27±\sqrt{729+4\times 28}}{2\left(-1\right)}
Multiply -4 times -1.
x=\frac{-27±\sqrt{729+112}}{2\left(-1\right)}
Multiply 4 times 28.
x=\frac{-27±\sqrt{841}}{2\left(-1\right)}
Add 729 to 112.
x=\frac{-27±29}{2\left(-1\right)}
Take the square root of 841.
x=\frac{-27±29}{-2}
Multiply 2 times -1.
x=\frac{2}{-2}
Now solve the equation x=\frac{-27±29}{-2} when ± is plus. Add -27 to 29.
x=-1
Divide 2 by -2.
x=-\frac{56}{-2}
Now solve the equation x=\frac{-27±29}{-2} when ± is minus. Subtract 29 from -27.
x=28
Divide -56 by -2.
-x^{2}+27x+28=-\left(x-\left(-1\right)\right)\left(x-28\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -1 for x_{1} and 28 for x_{2}.
-x^{2}+27x+28=-\left(x+1\right)\left(x-28\right)
Simplify all the expressions of the form p-\left(-q\right) to p+q.
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}