====== Question 6, Exercise 5.3 ======
Solutions of Question 6 of Exercise 5.3 of Unit 05: Polynomials. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. 

=====Question 6======
The volume of box is $y^3-2y^2-y+2$. If the length of one side $y-2$, find the length of the other two sides.

** Solution. **

Let volume of box $=p(y)=y^3-2y^2-y+2$

Length of one side = $y-2$.

This gives $y-2$ is factor of $p(y)$. Thus $2$ is zeros of $p(y)$

Using synthetic division:
\[
\begin{array}{r|rrrr}
2 & 1 & -2 & -1 & 2 \\
& \downarrow   & 2 & 0 & -2 \\
\hline
& 1  & 0  & -1 & 0 \\
\end{array}
\]
Thus 
\begin{align*}
p(y) & = (y-2)(y^2-1) \\
& = (y-2)(y+1)(y-1)
\end{align*}
Hence the length of remaining two sides are $y+1$ and $y-1$. GOOD m(

====Go to ====

<text align="left"><btn type="primary">[[math-11-nbf:sol:unit05:ex5-3-p5|< Question 4]]</btn></text>