Final answer:
After substituting x = -1 into the polynomial (x⁵ - 2x⁴ + 3x³- 5x² - 7x - 2), the result is -4, which means (x + 1) is not a factor of the polynomial. The answer to this question is NO.
Step-by-step explanation:
To determine if (x + 1) is a factor of the polynomial (x⁵ - 2x⁴ + 3x³- 5x² - 7x - 2), we can apply the Factor Theorem.
According to the Factor Theorem, (x + 1) is a factor if and only if substituting x = -1 into the polynomial yields a result of zero.
Let's substitute x = -1 into the polynomial: (-1)⁵ - 2(-1)⁴ + 3(-1)³ - 5(-1)²- 7(-1) - 2
= -1 - 2 - 3 - 5 + 7 - 2
= -4
Since substituting x = -1 into the polynomial does not yield zero, this implies that (x + 1) is not a factor of the polynomial in question.
Therefore, the answer to this question is NO, and there are no zeros corresponding to (x + 1) for this polynomial.