 Questions & Answers    Question Answers

# If one factor of ${a^4} + {\text{ }}{b^4} + {\text{ }}{a^2}{b^2}$ is ${a^2} + {\text{ }}{b^2} + {\text{ }}ab$, then the other factor is:${\text{A}}{\text{. }}{a^3} + {b^3} + {c^3}${\text{B}}{\text{. }}{a^2} + {b^2} - ab$ {\text{C}}{\text{. }}{a^2} + {b^2} + {c^2}$${\text{D}}{\text{. }}{{\text{a}}^2}{\text{ + }}{{\text{b}}^2}{\text{ + ab}}$  Answer Verified

Hint: Use long division method to divide ${a^4} + {b^4} + {a^2}{b^2}$ by the given factor ${a^2} + {b^2} + ab$ to find other factor.

Complete step by step answer:

We 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 ${a^2} + {b^2} + ab$ is a factor of ${a^4} + {b^4} + {a^2}{b^2}$

Now another factor is determined by long division method:

${a^2} + {b^2} + ab\mathop{\left){\vphantom{1\begin{gathered} {a^4} + {b^4} + {a^2}{b^2} - {a^2}{\text{ - }}{a^2}{b^2}{\text{ - }}{a^3}b \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ {b^4}{\text{ }} - {a^3}b {b^4}{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2} \_\_\_\_\_\_\_\_\_\_\_\_\_\_ - {a^3}b{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2} - {a^3}b{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2} \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ {\text{ }}0 \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \end{gathered} }}\right. \!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered} {a^4} + {b^4} + {a^2}{b^2} - {a^2}{\text{ - }}{a^2}{b^2}{\text{ - }}{a^3}b \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ {b^4}{\text{ }} - {a^3}b {b^4}{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2} \_\_\_\_\_\_\_\_\_\_\_\_\_\_ - {a^3}b{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2} - {a^3}b{\text{ }} - a{b^3}{\text{ }} - {a^2}{b^2} \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ {\text{ }}0 \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \end{gathered} }}} \limits^\,\,\, {{a^2} + {b^2} - ab}}$

Thus the another factor is ${a^2} + {b^2} - ab$

$\therefore$ The correct option is (b)

Note: - When one factor of the polynomial is given and asked us to find another polynomial we will factorise the given polynomial or use a long division method to find the solution.

Bookmark added to your notes.
View Notes
Steps to Comprehend and Summarize Text  Factorization of Algebraic Expressions  Algebraic Expressions  Addition and Subtraction of Algebraic Expressions  Algebraic Expressions Worksheet  Algebraic Expressions and Identities  Algebraic Expressions and Equations  Variables and Constants in Algebraic Expressions  CBSE Class 7 Maths Chapter 12 - Algebraic Expressions Formulas  Factor of 415  