Question

Which of the following best describes the relationship between (x²) and the polynomial 3x² - x - 14?

1) (x²) is a factor of the polynomial
2) (x²) is not a factor of the polynomial
3) (x²) is equal to the polynomial
4) The relationship between (x²) and the polynomial cannot be determined

Answer 1

The term (x²) is not a factor of the polynomial 3x² - x - 14, since the polynomial does not have (x²) as a common factor in all its terms, indicating that option 2 is correct.

Step-by-step explanation:

The relationship between (x²) and the polynomial 3x² - x - 14 can be determined by checking whether (x²) is a factor of the polynomial. For (x²) to be a factor, the polynomial must be divisible by (x²) without leaving a remainder.

In this case, since the polynomial 3x² - x - 14 cannot be factored to have (x²) as a factor, because its terms do not all have (x²) as a common factor, we can conclude that option 2, (x²) is not a factor of the polynomial, is the correct answer. The polynomial 3x² - x - 14 is a quadratic equation, which is an equation that can be written in the form ax² + bx + c = 0, but it does not have (x²) as a multiply repeated factor.