Question

Determine which expression could represent a polynomial with a factor of (* – √31).

A) x² + 31
B) x² - 31
C) x² - 31x
D) x² + 31x

Answer 1

An expression that could represent a polynomial with a factor of (x - √31) is x² - 31 because, when (x - √31) is squared, it results in x² - 2x√31 + 31, and the constant term is 31.

Step-by-step explanation:

To determine which expression could represent a polynomial with a factor of (x – √31), we need to consider how factors relate to polynomial expressions. A polynomial with a factor of (x – √31) would result in a term of √31 when multiplied out. Therefore, the corresponding term in the polynomial would be +31 when squared, because (√31)^2 = 31. The only expression that meets this criterion is x² – 31, as the other options either add or involve x, which would not result from squaring √31.