In This Chapter We cover the all the topics and basics of factorization these are the topics we cover as follows:

  • Highest Common Factor (H.C.F) of Monomials: The chapter introduces the concept of H.C.F. for algebraic terms. It defines the H.C.F. as the common factor that has the greatest coefficient and the highest powers of the variables.

  • Introduction to Factorization: Factorization is defined as the process of writing an algebraic expression as the product of two or more factors.

  • Algebraic Identities: The Chapter provides a comprehensive list of standard algebraic formulas (such as $a^2-b^2=(a+b)(a-b)$ and $a^3+b^3=(a+b)(a^2-ab+b^2)$) to help factorize complex expressions.

  • Splitting the Middle Term: The chapter details a specific technique for factorizing quadratic expressions in the form of $ax^2+bx+c$ by splitting the middle term.

  • Division of Algebraic Expressions: The final section applies factorization concepts to division. It covers four progression levels:

    • Division of a monomial by another monomial using factorization.

    • Division of a polynomial by a monomial using factorization.

    • Division of a polynomial by another polynomial using factorization.

    • Division of a polynomial by another polynomial using the Long Division method or a shortcut method.