What is the quotient when 3x^2 + 18x - 76 is divided by (x - 8)

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The quotient obtained when (3x^2 + 18x - 76) is divided by (x-8) has to be determined.

When f(x) is divided by (x-a), the remainder is given by f(a). If Q is the quotient `(f(x))/(x-a) = Q + (f(a))/(x-a)`

For f(x) = 3x^2 + 18x - 76, f(8) = 260. This gives the remainder obtained when (3x^2 + 18x - 76) is divided by (x-8) as 260

The quotient obtained during the same operation is `(3x^2 + 18x - 76 - 260)/(x-8)` = `(3x^2 + 18x - 336)/(x-8)` = 3x + 42.

To verify the result: (3x + 42)(x - 8) + 260 = 3x^2 + 18x - 76

The quotient obtained when (3x^2 + 18x - 76) is divided by (x-8) is 3x + 42.

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