Factorization of Cubic Polynomial MCQs Quiz | Class 9
Welcome to the Factorization of Cubic Polynomial MCQs Quiz for Class 9 Mathematics (Code 041). This quiz covers Unit II: Algebra, specifically focusing on the Factorization of Cubic Polynomials using the factor theorem to find one factor and then factorizing the remaining quadratic polynomial. Test your knowledge with these questions, submit your answers to see the score, and download the solution PDF for revision.
Overview of Cubic Polynomials
A cubic polynomial is an algebraic expression of degree 3. The standard form is p(x) = ax^3 + bx^2 + cx + d, where a is not equal to 0. Factorizing a cubic polynomial involves finding three linear factors whose product equals the original polynomial.
Steps to Factorize Using Factor Theorem
The most common method for Class 9 involves a combination of the Factor Theorem and division.
- Step 1: Find the first factor. Use the trial method by substituting values (like 1, -1, 2, -2) into the polynomial p(x). If p(a) = 0, then (x – a) is a factor.
- Step 2: Divide the polynomial. Divide the cubic polynomial p(x) by the linear factor found in Step 1 using long division. The quotient will be a quadratic polynomial.
- Step 3: Factorize the quadratic. Use the “splitting the middle term” method to factorize the quotient into two more linear factors.
- Step 4: Final Answer. Combine all three factors to get the complete factorization.
Key Formulas & Concepts
| Concept | Description |
|---|---|
| Factor Theorem | If p(a) = 0, then (x – a) is a factor of p(x). |
| Constant Term Factors | Possible roots are usually factors of the constant term ‘d’ in the polynomial. |
| Degree & Factors | A cubic polynomial (degree 3) has at most 3 real linear factors. |
Quick Revision Notes
- Always look for a common factor first (e.g., pulling out x if the constant term is 0).
- Check p(1) by summing coefficients. If sum is 0, (x – 1) is a factor.
- Check p(-1) by summing coefficients of even powers vs odd powers.
Extra Practice Questions
- Factorize: x^3 – 6x^2 + 11x – 6. (Hint: Try x=1)
- Check if (x+1) is a factor of x^3 + x^2 + x + 1.
- Find the value of k if (x-1) is a factor of 4x^3 + 3x^2 – 4x + k.
- Factorize y^3 – 7y + 6.
- Expand (3x – 2)(x – 1)(x + 2).
Content created and reviewed by the CBSE Quiz Editorial Team based on the latest NCERT textbooks and CBSE syllabus. Our goal is to help students practice concepts clearly, confidently, and exam-ready through well-structured MCQs and revision content.