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Question
x^{3}-13x-12
Factor the expression
\left(x-4\right)\left(x+1\right)\left(x+3\right)
Evaluate
x^{3}-13x-12
Calculate
x^{3}+4x^{2}+3x-4x^{2}-16x-12
Rewrite the expression
x\times x^{2}+x\times 4x+x\times 3-4x^{2}-4\times 4x-4\times 3
\text{Factor out }x\text{ from the expression}
x\left(x^{2}+4x+3\right)-4x^{2}-4\times 4x-4\times 3
\text{Factor out }-4\text{ from the expression}
x\left(x^{2}+4x+3\right)-4\left(x^{2}+4x+3\right)
\text{Factor out }x^{2}+4x+3\text{ from the expression}
\left(x-4\right)\left(x^{2}+4x+3\right)
Solution
More Steps
Evaluate
x^{2}+4x+3
Rewrite the expression
x^{2}+\left(3+1\right)x+3
Calculate
x^{2}+3x+x+3
Rewrite the expression
x\times x+x\times 3+x+3
\text{Factor out }x\text{ from the expression}
x\left(x+3\right)+x+3
\text{Factor out }x+3\text{ from the expression}
\left(x+1\right)\left(x+3\right)
\left(x-4\right)\left(x+1\right)\left(x+3\right)
Show Solutions
Find the roots
x_{1}=-3,x_{2}=-1,x_{3}=4
Evaluate
x^{3}-13x-12
To find the roots of the expression,set the expression equal to 0
x^{3}-13x-12=0
Factor the expression
\left(x-4\right)\left(x+1\right)\left(x+3\right)=0
\text{Separate the equation into }3\text{ possible cases}
\begin{align}&x-4=0\\&x+1=0\\&x+3=0\end{align}
Solve the equation
More Steps
Evaluate
x-4=0
Move the constant to the right-hand side and change its sign
x=0+4
Removing 0 doesn't change the value,so remove it from the expression
x=4
\begin{align}&x=4\\&x+1=0\\&x+3=0\end{align}
Solve the equation
More Steps
Evaluate
x+1=0
Move the constant to the right-hand side and change its sign
x=0-1
Removing 0 doesn't change the value,so remove it from the expression
x=-1
\begin{align}&x=4\\&x=-1\\&x+3=0\end{align}
Solve the equation
More Steps
Evaluate
x+3=0
Move the constant to the right-hand side and change its sign
x=0-3
Removing 0 doesn't change the value,so remove it from the expression
x=-3
\begin{align}&x=4\\&x=-1\\&x=-3\end{align}
Solution
x_{1}=-3,x_{2}=-1,x_{3}=4
Show Solutions
