Calculate the square root of the polynomial: $4 x^{4} + 16 x^{3} + 8 x^{2} - 16 x + 4$ (Use division method).

2 x^{2} + 4 x - 2

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∣ ∣ 2 x^{2} - 4 x - 2 ∣ ∣

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2 x^{2} - 4 x - 2

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∣ ∣ 2 x^{2} + 4 x - 2 ∣ ∣

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Solution

The correct option is D $∣ ∣ 2 x^{2} + 4 x - 2 ∣ ∣$
$\div$ $2 x^{2} + 4 x - 2$ <= Quotient
$2 x^{2}$
$4 x^{4} + 16 x^{3} + 8 x^{2} - 16 x + 4$
$4 x^{4}$
$4 x^{2} + 4 x$ $16 x^{3} + 8 x^{2}$
$16 x^{3} + 16 x^{2}$
$4 x^{2} + 8 x - 2$ $- 8 x^{2} - 16 x + 4$
$- 8 x^{2} - 16 x + 4$
Remainder $\Rightarrow 0$
The square root of $4 x^{4} + 16 x^{3} + 8 x^{2} - 16 x + 4$ is $∣ ∣ 2 x^{2} + 4 x - 2 ∣ ∣$

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