Question

Coefficient of $x^2$ in the expansion of $(x^2 + x - 2)^5$ is

• A. 800
• B. 756
• C. 0
• D. 512

Hint:

Consider the powers of each term carefully; sometimes desired power terms may not exist in expansions.

Answer 1

The Correct Option is C

Expand $(x^2 + x - 2)^5$. To get the coefficient of $x^2$, consider terms where the powers of $x$ sum to 2. Possible terms are: - $(x^2)^1 \times (x)^0 \times (-2)^4$ with total power $2 \times 1 = 2$, - $(x^2)^0 \times (x)^2 \times (-2)^3$ but $x^2$ term requires $x$ squared, - and so on. After checking all combinations, there is no term with exact $x^2$ power because powers come in even multiples or higher. Therefore, coefficient of $x^2$ is zero.