Use long division to determine the quotient of the polynomials. (x3 – 7x – 6) ÷ (x – 4) Which of the following options best desc
ribes the relationship between the polynomial division and the remainder? The quotient has a remainder of zero. Therefore, the divisor is a factor of the dividend. The quotient has a remainder of 9. Therefore, the divisor is not a factor of the dividend. The quotient has a remainder of 30. Therefore, the divisor is not factor of the dividend. The quotient has a remainder of 36. Therefore, the divisor is a factor of the dividend.
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This system has exactly one solution, because the two equation are linearly independent (i.e. one is not a multiple of the other).
We can explicitly find the solutions: from the first equation we deduce
Plug this value for x in the second equation:
Multiply both sides by 6 to get
Plug this value for y in the expression for x:
Since both a,b are not zero, both solutions are well defined.