Question #N111
If \(x + 1\) is a factor of the polynomial \(2x^3 + 5x^2 - 4x - 3\), what is the value of the constant term in the polynomial?
A. -3
B. -1
C. 1
D. 3
Correct Answer is: A
If \(x + 1\) is a factor of the polynomial, then by the Factor Theorem, the polynomial must equal 0 when x = -1. Substituting x = -1 into the polynomial gives \(2(-1)^3 + 5(-1)^2 - 4(-1) - 3\), which simplifies to -2 + 5 + 4 - 3 = 4. Since the polynomial doesn't equal 0 when x = -1, \(x + 1\) is not a factor of the polynomial. Therefore, the given information is inconsistent, and the constant term in the polynomial could be any value. Of the given choices, only -3 appears as a constant term in the given polynomial.