VerifiedWe know that, if we are provided with a factor of a number and we have to find another factor we simply divide the number by the given factor.
For example we know that 3 is one of a factor of 12 and we have to find another factor we simply divide
12 by 3 to know another factor i.e, $\dfrac{{12}}{3} = 4$
Thus, 4 is another factor of 12.
In the similar way we will find the factor of given question
Given that ${a^2} + {b^2} + ab{\text{ is a factor of }}{a^4} + {b^4} + {a^2}{b^2}$
Now another factor is determined by following method:
$
{a^2} + {b^2} + ab\mathop{\left){\vphantom{1\begin{gathered}
{a^4} + {b^4} + {a^2}{b^2}
- {a^2}{\text{ - }}{a^2}{b^2}{\text{ - }}{a^3}b
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
{b^4}{\text{ }} - {a^3}b
{b^4}{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2}
\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- {a^3}b{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2}
- {a^3}b{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2}
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
}}0
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
{a^4} + {b^4} + {a^2}{b^2}
- {a^2}{\text{ - }}{a^2}{b^2}{\text{ - }}{a^3}b
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
{b^4}{\text{ }} - {a^3}b
{b^4}{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2}
\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- {a^3}b{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2}
- {a^3}b{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2}
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
}}0
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
\end{gathered} }}}
\limits^{\displaystyle \,\,\, {{a^2} + {b^2} - ab}}
$
Thus the another factor is {a^2} + {b^2} - ab
Hence, the correct option is (b)
Note: - In these types of questions we simply divide the given factor with the given polynomial.
