Divide the polynomial: 8x4−4x3+2x22x2

Answer 1

To divide the polynomial \( 8x^4 - 4x^3 + 2x^2 \) by \( 2x^2 \), you can perform polynomial long division or simply divide each term in the dividend by the divisor.

Let's divide each term:

1. \( \frac{8x^4}{2x^2} = 4x^2 \)
2. \( \frac{-4x^3}{2x^2} = -2x \)
3. \( \frac{2x^2}{2x^2} = 1 \)

Now combine the results:

\[ 4x^2 - 2x + 1 \]

So, the quotient of the division \( \frac{8x^4 - 4x^3 + 2x^2}{2x^2} \) is:

\[ 4x^2 - 2x + 1 \]