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Is (x + 1) a factor of (x ^ 5 - 2x ^ 4 + 3x ^ 3 - 5x ^ 2 - 7x - 2)' ? YES or NO List 1 zero (if applicable).​

User Nicky
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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.

User Abhishek Patidar
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