Final answer:
To compute the quotient of (x²−14x+48)/(x−8), long division is used, resulting in a quotient of x−6. Option C is correct.
Step-by-step explanation:
To find the quotient of the division (x²−14x+48)/(x−8), perform long division:
Divide the first term of the numerator by the first term of the denominator: x² divided by x, which equals x.
Multiply the entire divisor (x−8) by x and subtract the result from the numerator. This gives us: x(x−8) which is x²−8x. Subtract this from the numerator: (x²−14x+48)−(x²−8x) = −6x+48.
Repeat the process. Divide −6x by x to get −6. Then, multiply (x−8) by −6 and subtract the result from −6x+48, which gives: −6(x−8) = −6x+48 and subtract this to get 0, meaning there's no remainder.
The result is x−6, which corresponds to option c.