Notes, solutions of unit 05, General Mathematics 9, for Punjab Curriculum & Textbook Board (PCTB), Lahore.

* Recall factorization of expressions of the following types.

  • $ka + kb + kc$
  • $ac + ad + bc + bd$
  • $a^2 \pm 2ab + b^2$
  • $a^2 – b^2$
  • $a^2 \pm 2ab + b^2 – c^2$
  • Factorize the expressions of the following types.
  • Type I:
  • $ a^4 + a^2b^2 + b^4 or a^4 + 4b^4$
  • Type II:
  • $ x^2 + px + q$
  • Type III:
  • $ax^2 + bx + c$
  • Type IV:
  • $(ax^2 + bx + c) (ax^2 + bx + d) + k$
  • $(x + a) (x + b) (x + c) (x + d) + k$
  • (x + a) (x + b) (x + c) (x + d) + kx^2$
  • Type V:
  • $a^3 + 3a^2b + 3ab^2 + b^3$
  • $a^3 − 3a^2b + 3ab^2 − b^3$
  • Type VI:
  • $a^3 + b^3$
  • State and prove remainder theorem and explain through examples.
  • Find Remainder (without dividing) when a polynomial is divided by a linear polynomial.
  • Define zeros of a polynomial.
  • State and prove Factor theorem.
  • Use Factor theorem to factorize a cubic polynomial.