Divide Using Long Polynomial Division (4x^5-x^3+7)/(2x^5+x^2)

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of ${\displaystyle 0}$.

Divide the highest order term in the dividend ${\displaystyle 4x^5}$ by the highest order term in divisor ${\displaystyle 2x^5}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle 4x^5+0+0+2x^2+0+0}$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.