Using division method find the square root of $x^{4} - 6 x^{3} + 19 x^{2} - 30 x + 25$

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Solution

$\div$ $x^{2} - 3 x + 5$ <= Quotient
$x^{2}$
$x^{4} - 6 x^{3} + 19 x^{2} - 30 x + 25$
$x^{4}$
$2 x^{2} - 3 x$ $- 6 x^{3} + 19 x^{2}$
$- 6 x^{3} + 9 x^{2}$
$2 x^{2} - 6 x + 5$ $10 x^{2} - 30 x + 25$
$10 x^{2} - 30 x + 25$
Remainder $\Rightarrow 0$
The square root of $x^{4} - 6 x^{3} + 19 x^{2} - 30 x + 25$ is $∣ ∣ x^{2} - 3 x + 5 ∣ ∣$

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