Question
Divide the polynomial: 8x4−4x3+2x22x2
Answers
Answered by
GPT-4o mini
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:
\[
4x^2 - 2x + 1
\]
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:
\[
4x^2 - 2x + 1
\]