Question

If (x+3)is the factor of polynomial x³+ax²+x+3 then a is​

Answer 1

Step-by-step explanation:

Question :

If (x+3) is the factor of polynomial x³+ax²+x+3 then, the value of a is :

To find:

The value of a =?

\large\sf{\color{green} SOLUTION :}SOLUTION:

\hspace{3em}\implies \bf \: x + 3 = 0⟹x+3=0

\begin{gathered} \\ \hspace{3em} \implies \bf \: x = - 3 \: \: \: ....put \: the \: value \: in \: equation\end{gathered}

⟹x=−3....putthevalueinequation

\quad\implies \displaystyle \sf \: {x}^{3} + {ax}^{2} + x + 3 = 0⟹x

3

+ax

2

+x+3=0

\begin{gathered} \\ \quad \implies \sf \: {( - 3)}^{3} + a {( - 3)}^{2} + ( - 3) + 3 = 0\end{gathered}

⟹(−3)

3

+a(−3)

2

+(−3)+3=0

\quad \implies \sf \: - 27 + 9a \cancel{ - 3 + 3} = 0⟹−27+9a

−3+3

=0

\begin{gathered} \\ \quad \implies \sf \: - 27 = - 9a\end{gathered}

⟹−27=−9a

\begin{gathered} \\ \quad \implies \sf \: a = \frac{27}{9} = \cancel \frac{27}{9} = 3\end{gathered}

⟹a=

9

27

=

9

27

=3

\: \qquad \therefore \boxed{ \underline{ \bf{the \: value \: of \: a \: is \: 3}}}∴

thevalueofais3