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

  1. Factorize: 2x^2 + 7x + 3
  2. Factorize: 6x^2 + 5x – 6
  3. Find the value of k if (x-1) is a factor of 4x^3 + 3x^2 – 4x + k.
  4. Factorize using splitting the middle term: y^2 – 5y + 6
  5. Check if (x+2) is a factor of x^3 + 3x^2 + 3x + 1.