Factorization of Quadratic Polynomial MCQs Quiz | Class 9
This quiz covers Unit II: Algebra for Class IX Mathematics (Code 041). It focuses on the factorization of quadratic polynomials of the form ax^2 + bx + c (where a is not 0), utilizing the splitting the middle term method and the Factor Theorem. Test your understanding, view the correct solutions, and download your results as a PDF.
Overview of Factorization of Quadratic Polynomials
In Class IX Mathematics (Unit II: Algebra), factorizing quadratic polynomials is a fundamental skill. A quadratic polynomial generally takes the form ax^2 + bx + c, where a, b, and c are real numbers and a is not equal to zero.
Key Methods
There are two primary ways to factorize these polynomials covered in this syllabus:
1. Splitting the Middle Term
To factorize ax^2 + bx + c, we look for two numbers, say p and q, such that:
- Sum (p + q) = b (the coefficient of x)
- Product (pq) = ac (the product of the coefficient of x^2 and the constant term)
Once p and q are found, we rewrite the middle term bx as px + qx and group terms to find common factors.
2. Factor Theorem
If p(x) is a polynomial and p(a) = 0, then (x – a) is a factor of p(x). Conversely, if (x – a) is a factor, then p(a) = 0. This is useful for checking potential factors derived from the constant term.
Quick Revision Table
| Expression Form | Factor Pattern | Example |
|---|---|---|
| x^2 + (a+b)x + ab | (x + a)(x + b) | x^2 + 5x + 6 = (x+2)(x+3) |
| x^2 – (a+b)x + ab | (x – a)(x – b) | x^2 – 5x + 6 = (x-2)(x-3) |
| x^2 + (a-b)x – ab | (x + a)(x – b) | x^2 + x – 6 = (x+3)(x-2) |
Extra Practice Questions
- Factorize: 2x^2 + 7x + 3
- Factorize: 6x^2 + 5x – 6
- Find the value of k if (x-1) is a factor of 4x^3 + 3x^2 – 4x + k.
- Factorize using splitting the middle term: y^2 – 5y + 6
- Check if (x+2) is a factor of x^3 + 3x^2 + 3x + 1.
