Question

Find the square root of the following polynomial by division method: $x^4-8x^3+8x^2+4x+1$

• A. $|2x^2+2x+1|$
• B. $|2x^2-2x+1|$
• C. $|2x^2+2x-1|$
• D. None of these

Answer 1

Answer: (A)

$|2x^2+2x+1|$

We find the square root of the given polynomial $4x^4-8x^3+8x^2+4x+1$ by following the steps shown below:

Step 1. Compute the square root of the leading term $\left(4x^4\right)$ and put it, $\left(2x^2\right)$, in the two places shown.

Step 2. Subtract and bring down the next two terms.

Step 3. Double the currently displayed quotient $\left(2x^2\right)$ to $4x^2$. Then add a new term, $x$, to the quotient such that the result will remove the first term, $(-8x^3)$, in the current partial remainder.

Step 4. Repeat steps 2 and 3 until done.

The division is as follows:

Hence, the square root of $4x^4-8x^3+8x^2+4x+1$ is $2x^2+2x+1$.