Use long division to determine the quotient of the polynomials. (x3 – 7x – 6) ÷ (x – 4) Which of the following options best describes the relationship between the polynomial division and the remainder? a. The quotient has a remainder of zero. Therefore, the divisor is a factor of the dividend. b. The quotient has a remainder of 9. Therefore, the divisor is not a factor of the dividend. c. The quotient has a remainder of 30. Therefore, the divisor is not factor of the dividend. d. The quotient has a remainder of 36. Therefore, the divisor is a factor of the dividend.

Answer:The correct option is c.Step-by-step explanation:The quotient of the polynomials is[tex]\frac{(x^3-7x-6)}{x-4}[/tex]We need to find the remainder by using long division method.The dividend of the given expression is[tex]Dividend=x^3-7x-6[/tex][tex]Divisor=x-4[/tex]The long division method is shown below.[tex]\frac{(x^3-7x-6)}{x-4}=(x^2+4x+9)+\frac{30}{x-4}[/tex]From the below attachment it is clear that the quotient has a remainder of 30. Therefore, the divisor is not factor of the dividend. Therefore the correct option is c.