Unit 05: Factorization: Online View

On this page, online view of the notes of unit 05 are given. After studying this unit , the students will be able to:

  1. Recall factorization of expressions of the following types.
  2. $ka + kb + kc$
  3. $ac + ad + bc + bd$
  4. $a^2 + 2ab + b^2$
  5. $a^2 – b^2$
  6. $a^2 + 2ab + b^2 – c^2$
  7. Factorize the expressions of the following types.
  8. Type I:$a^4 + a^2b^2 + b^4$ or $a^4 + 4b^4$
  9. Type II:$x^2 + px + q$
  10. Type III:$ax^2 + bx + c$
  11. Type IV:$(ax^2 + bx + c) (ax2 + bx + d) + k$
    $(x + a) (x + b) (x + c) (x + d) + k$
    $(x + a) (x + b) (x + c) (x + d) + kx^2$
  12. Type V:$a^3 + 3a^2b + 3ab^2 + b^3$
    $a^3 − 3a^2b + 3ab^2 − b^3$
  13. Type VI:

$a^3 + b^3$

  1. State and prove remainder theorem and explain through examples.
  2. Find Remainder (without dividing) when a polynomial is divided by a linear polynomial.
  3. Define zeros of a polynomial.
  4. State and prove Factor theorem.
  5. Use Factor theorem to factorize a cubic polynomial.

Please select the Exercise from the list given below.