Final answer:
To determine the remaining factors of x³ - 6x² - x - 30 given that (x - 5) is a factor, one must divide the given polynomial by (x - 5). The result would be a quadratic polynomial, which when multiplied back with (x - 5), should yield the original polynomial. The correct choice(s) out of the options would provide this result upon multiplication. Option number d is correct.
Step-by-step explanation:
The student has asked for the remaining factors of x³ - 6x² - x - 30, given that (x - 5) is a factor. To find the remaining factors, we can perform polynomial long division or use synthetic division to divide the polynomial by (x - 5). Doing so, we would find the quotient polynomial, which, when multiplied by (x - 5), gives us the original polynomial, x³ - 6x² - x - 30.
Upon division, we would get a quadratic polynomial. Since the student did not provide a step to find the quotient, we can't solve this directly. However, we can check the given options for the correct one by performing a multiplication of the factors listed with (x - 5) and see if it matches the initial polynomial. The quadratic that yields the original polynomial when multiplied by (x - 5) would be the set of remaining factors from the choices a) through d).