Binomial Theorem
Grade 11
Question:
<p>Coefficient of x<sup>5</sup> in the expansion of (1 + x + x<sup>2</sup>)<sup>15</sup> is:</p>
<p style="display:inline">3<span class="math-tex">\(\cdot\)</span><sup>16</sup>C<sub>4</sub> + <sup>16</sup>C<sub>5</sub></p>
<p style="display:inline"><sup>16</sup>C<sub>5</sub></p>
<p style="display:inline"><sup>15</sup>C<sub>3</sub> + <sup>15</sup>C<sub>4</sub></p>
<p style="display:inline"><sup>15</sup>C<sub>5</sub></p>
Step-by-Step Solution
Key Concept: Use the multinomial theorem to sum the coefficients for all non-negative integer solutions where the powers of the terms add up to the total expansion power and the desired exponent.
<p>3<span class="math-tex">$\cdot$</span><sup>16</sup>C<sub>4</sub> + <sup>16</sup>C<sub>5</sub></p>
Correct Answer: A