Discussion
The coefficient of \(x^{4}\) in the polynomial \((x - 1)^{3}(x - 2)^{3}\) is equal to _______.
Answer: A
The coefficient of \(x^{4}\) is 33.
Combine the factors first: \((x - 1)^{3}(x - 2)^{3} = (x^{2} - 3x + 2)^{3}\). An \(x^{4}\) term arises when the three factors contribute powers adding to 4:
\[ \begin{aligned} x^{2} \cdot x^{2} \cdot 2 &: \ 3 \times 2 = 6 \\ x^{2} \cdot (-3x)(-3x) &: \ 3 \times 9 = 27 \\ \text{total} &= 6 + 27 = 33 \end{aligned} \]
The 3 in each line counts the ways of choosing which factor supplies the odd term. Every term contributing to \(x^{4}\) is positive (the two negative factors of \(-3x\) multiply to a positive), so a negative answer such as −3 is impossible, and 30 and 21 each miss part of the count.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development