Answer
The factors for the given equation ${{x}^{2}}+6x+8=0$ are $x+2=0$and $x+4=0$, and the values of $x=-4,-2$.
Work Step by Step
The equation is ${{x}^{2}}+6x+8=0$.
Below steps to be followed during the method of factorization.
Rule 1: Arrange the equation in the decreasing order of power of\[x\] as:
${{x}^{2}}+6x+8=0$
Rule 2: Split the middle term that is term of \[x\]as sum or difference of two terms and the product of these two terms is equal to product of constant and the first term (i.e.,${{x}^{2}}$ ).
$\begin{align}
& {{x}^{2}}+6x+8=0 \\
& {{x}^{2}}+4x+2x+8=0
\end{align}$
Rule 3: Taking the x common in first two terms and a constant number common in second two terms.
$\begin{align}
& {{x}^{2}}+6x+8=0 \\
& {{x}^{2}}+4x+2x+8=0 \\
& x\left( x+4 \right)+2\left( x+4 \right)=0 \\
& \left( x+2 \right)\left( x+4 \right)=0
\end{align}$
These are the obtained factors for the given equation.
Rule 4: Equating each factor to zero as:
$\begin{align}
& x+2=0 \\
& x+4=0
\end{align}$
The values of\[x\]or roots of equation are $x=-4,-2$.
The factors for the given equation ${{x}^{2}}+6x+8=0$ are $x+2=0$and $x+4=0$, and the values of $x=-4,-2$.
