Class 9th Maths NCERT chapter 02 Polinomials Exercise 2.3 question number 3 & 4

For an exercise on factorization in Chapter 2.3 "Polynomials," here's a possible description:
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*Exercise 2.3: Factorization*
In this exercise, you will practice the factorization of polynomials. Factorization is the process of expressing a polynomial as a product of its factors. It is an essential skill in algebra that simplifies solving polynomial equations and understanding their properties.
*Objectives:*
1. To learn how to factorize different types of polynomials, including:
Common monomial factors
Difference of squares
Perfect square trinomials
Trinomials of the form \(ax^2 + bx + c\)
2. To apply factorization techniques to solve polynomial equations.
*Instructions:*
1. *Identify Common Factors:* Begin by identifying and factoring out the greatest common factor (GCF) from each term in the polynomial.
2. *Factor by Grouping:* For polynomials with four or more terms, group terms to find common factors and simplify the expression.
3. *Factor Special Products:* Recognize and factor special products such as the difference of squares (\(a^2 - b^2 = (a - b)(a + b)\)), perfect square trinomials (\(a^2 \pm 2ab + b^2 = (a \pm b)^2\)), and sum/difference of cubes.
4. *Quadratic Trinomials:* Factor quadratic trinomials using methods such as trial and error, splitting the middle term, or applying the quadratic formula.
5. *Verify Your Factors:* Multiply the factors to ensure they give the original polynomial.
*Example Problems:*
1. Factorize \(2x^2 + 4x\).
2. Factorize \(x^2 - 16\).
3. Factorize \(x^2 + 6x + 9\).
4. Factorize \(3x^2 + 11x + 6\).
*Hints:*
Always check for a GCF before applying other factorization techniques.
For quadratic trinomials, find two numbers that multiply to \(ac\) (the product of the coefficient of \(x^2\) and the constant term) and add to \(b\) (the coefficient of \(x\)).
*Practice these problems to master the skill of factorizing polynomials, which will be useful in solving more complex algebraic equations.*
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