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If the coefficients of x² and x³ are both zero, in the expansion of the expression (1 + ax + bx²)(1 − 3x)¹⁵ in powers of x, then the ordered pair (a,b) is equal to:

1. (28, 88)
2. (28, 315)
3. (-21, 714)
4. (-54, 315)

Correct answer: (28, 315)

Solution

The coefficients of x² and x³ in the expansion must be zero, which leads to a system of equations involving a and b. Solving these equations reveals that the only values that satisfy both conditions are a = 28 and b = 315.

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