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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.

Respuesta :

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.

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