Final answer:
The task is to verify if the expression (x^6 - 5)/(x - 5) is the quotient of the provided polynomial division (3x^2 + x - 35)/(x - 5). The solution involves polynomial division and application of rules for negative exponents and addition of exponents, followed by simplification of the resultant expression to check equivalence.
Step-by-step explanation:
The question asks to determine whether the expression x^6 - 5/x - 5 is the quotient of the given polynomial division (3x^2 + x - 35)/(x - 5). To find this out, we can perform polynomial long division or synthetic division. However, there is a typographical error in the expression which should be addressed; typically, the notation would imply division by 'x', subtraction of 5, which is likely not the intended meaning. Assuming the correct expression to analyze is (x^6 - 5)/(x - 5), we would then proceed to divide the two polynomials.
As a tip to solve similar problems, remember that when dividing polynomials, each term in the numerator is divided by the denominator and don't forget to apply the negative exponents rule, which states that the negative exponent denotes a division rather than a multiplication - flipping the term with the negative exponent to the denominator. Also, simplify using the add the exponents rule when multiplying terms with the same base.
To check if the provided quotient is correct, we would expand and simplify the numerator and then divide it by the denominator, verifying if the expressions are equivalent. Simplification could involve eliminating terms or reducing the expression to see if it matches the given quotient.