====== Question 2 and 3, Exercise 5.1 ======
Solutions of Question 2 and 3 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 2====
Show that $x-3$ is a factor of $x^{3}-2 x^{2}-5 x+6$.

** Solution. **

Let $p(x)=x^{3}-2 x^{2}-5 x+6$ and $x-c=x-3$ $\implies c=3$.

By factor theorem $x-3$ is factor of $p(x)$ iff $p(3)=0$.

Now 
\begin{align*}
p(3)&=3^3-2(3)^2-5(3)+6 \\
& = 27-18-15+6 \\
& = 0.
\end{align*}
Hence, $x-3$ is factor of $p(x)$. GOOD

=====Question 3=====
Decide whether $x-3$ is a factor of $x^{3}-2 x^{2}-5 x+1$ or not.

** Solution. **

Let $p(x)=x^{3}-2 x^{2}-5 x+1$ and $x-c=x-3$ $\implies c=3$.

By factor theorem $x-3$ is factor of $p(x)$ iff $p(3)=0$.

Now 
\begin{align*}
p(3)&=3^3-2(3)^2-5(3)+1 \\
& = 27-18-15+1 \\
& = -5 \neq 0
\end{align*}
Hence, $x-3$ is not factor of $p(x)$. GOOD
====Go to ====

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