1. What is the constant term in the expansion of (x3-x+3)(x2+2x-4)?答案是多少？為什麼？

[Q]
What is the constant term in the expansion of (x³ - x + 3)(x² + 2x - 4)?

[A]
The constant term in the expansion of (x³ - x + 3)(x² + 2x - 4)
is (0³ - 0 + 3)[0² + 2(0) - 4] = (3)(-4) = -12.

[Reason]
For any polynomial (多項式) f(x) = an x^n + a_(n-1) x^(n - 1) + ... + a3 x³ + a2 x² + a1 x + a0, the constant term is a0, which can be calculated by putting x = 0 in the expression, i.e. f(0) = a0.

+3x-4=12