# 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:

- Recall factorization of expressions of the following types.
- $ka + kb + kc$
- $ac + ad + bc + bd$
- $a^2 + 2ab + b^2$
- $a^2 – b^2$
- $a^2 + 2ab + b^2 – c^2$
- 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:$(ax^2 + bx + c) (ax2 + bx + d) + k$

$(x + a) (x + b) (x + c) (x + d) + k$

$(x + a) (x + b) (x + c) (x + d) + kx^2$ - 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.

Please select the Exercise from the list given below.

**Solutions of Unit 05**| Click to view if not visible