Factor
\left(-x-1\right)\left(x-1\right)\left(x^{2}+2\right)
Evaluate
2-x^{2}-x^{4}
Graph
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-x^{4}-x^{2}+2=0
To factor the expression, solve the equation where it equals to 0.
±2,±1
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 2 and q divides the leading coefficient -1. List all candidates \frac{p}{q}.
x=-1
Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
-x^{3}+x^{2}-2x+2=0
By Factor theorem, x-k is a factor of the polynomial for each root k. Divide -x^{4}-x^{2}+2 by x+1 to get -x^{3}+x^{2}-2x+2. To factor the result, solve the equation where it equals to 0.
±2,±1
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 2 and q divides the leading coefficient -1. List all candidates \frac{p}{q}.
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To factor the expression, solve the equation where it equals to 0.
\left(x+1\right)\left(-x+1\right)\left(x^{2}+2\right)
Rewrite the factored expression using the obtained roots. Polynomial x^{2}+2 is not factored since it does not have any rational roots.
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}