# Linear Factorization of x^4 +x^3 +5x -10

Linear Factorization of ${x}^{4}+{x}^{3}+5x-10$
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Step 1
Given quartic equation is :
${x}^{4}+{x}^{3}+5x-10=0$
Let us first take x common,
${x}^{4}+{x}^{3}+5x-10=0$
$⇒x\left({x}^{3}+{x}^{2}+5\right)-10=0$
$⇒x\left({x}^{3}+{x}^{2}+5\right)=10$
$⇒x=10,\left({x}^{3}+{x}^{2}+5\right)=10$
Step 2
Now,
${x}^{3}+{x}^{2}+5=10$
$⇒{x}^{2}\left(x+1\right)=5$
$⇒{x}^{2}=5,\left(x+1\right)=5$
Again,
${x}^{2}=5$
$⇒x=±5i$
and , x+1=5
$⇒x=4$
Step 3
The roots are : $10,4,±5i$