Find the Remainder (2x^7-3x^5+5x^3-7x^2)/(x^7+x^5+x^3+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 ${\displaystyle 2x^7}$ by the highest order term in divisor ${\displaystyle x^7}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle 2x^7+0+2x^5+0+2x^3+2x^2+0+0}$

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

The final answer is the quotient plus the remainder over the divisor.