Question

What must be added to the Polynomial $11y^3+5y^4+6y^5-3y^2+y+5$, so that the resulting polynomial is exactly divisible by $3y^2-2y+4$?

Answer 1

Let us divide the given polynomial $11y^3+5y^4+6y^5-3y^2+y+5$ or $6y^5+5y^4+11y^3-3y^2+y+5$ by $3y^2-2y+4$ as shown in the above image:

From the division, we get that the quotient is $2y^3+3y^2+3y-3$ and the remainder is $(-17y+17)$.

Hence $-(-17y+17)=17y-17$ should be added to $11y^3+5y^4+6y^5-3y^2+y+5$ so that the resulting polynomial is exactly divisible by $3y^2-2y+4$.