Unit 05 Consumer Mathematics (General Mathematics 9 PCTB)
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.
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