Find the square root of the polynomial: $9 x^{4} + 12 x^{3} + 28 x^{2} + 16 x + 16$ using division method.

x^{2} - 3 x + 5

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∣ ∣ x^{2} - 3 x + 5 ∣ ∣

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∣ ∣ x^{2} + 3 x + 5 ∣ ∣

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x^{2} + 3 x + 5

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Solution

The correct option is C $∣ ∣ x^{2} - 3 x + 5 ∣ ∣$
$\div$ $x^{2} - 3 x + 5$ <= Quotient
$3 x^{2}$
$9 x^{4} + 12 x^{3} + 28 x^{2} + 16 x + 16$
$9 x^{4}$
$6 x^{2} + 2 x$ $12 x^{3} + 28 x^{2}$
$12 x^{3} + 4 x^{2}$
$6 x^{2} + 4 x + 4$ $24 x^{2} + 16 x + 16$
$24 x^{2} + 16 x + 16$
Remainder $\Rightarrow 0$
The square root of $9 x^{4} + 12 x^{3} + 28 x^{2} + 16 x + 16$ is $∣ ∣ x^{2} - 3 x + 5 ∣ ∣$

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(x^{3} - x^{2} - 3 x + 5) \div (x - 1)

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