====== Question 4 and 5, Exercise 5.1 ======
Solutions of Question 4 and 5 of Exercise 5.1 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 4=====
If $4 y^{3}-4 y^{2}+10+2 y$ is completely divisible by any of its factor such that the quotient is $4 y^{2}-8 y+10$, then find other factor.

** Solution. **







=====Question 5=====
Find the value of ' $q$ ' if $x^{3}+q x^{2}-7 x+6$ is exactly divisible by $(x+1)$.

** Solution. **

Let $p(x)=x^{3}+q x^{2}-7 x+6$ and $x-c=x+1$ $\implies c=-1$.

By factor theorem $x+1$ is factor of $p(x)$ iff $p(-1)=0$.

This gives
\begin{align*}
&(-1)^3+q(-1)^2-7(-1)+6=0 \\
-&1+q+7+6=0\\
&q+12=0\\
&q=-12
\end{align*}








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