Answer :
Final answer:
To determine the quotient and remainder of the polynomial using long division, we divide the terms of the dividend by the divisor one by one. In this case, the quotient is x - 8/x² + 72x/x and the remainder is 0.
Explanation:
To use long division to determine the quotient and remainder of a polynomial, we divide the terms of the dividend by the divisor one by one. Divide x³ by x² to get x as the first term of the quotient. Then, we multiply the entire divisor by x and subtract it from the dividend. We continue this process until we have divided all terms of the dividend.
In the case of f(x) = x³ - 11x² + 40x - 48, divide x³ by x² to get x as the first term of the quotient. Multiply x² - 11x by x and subtract it from the dividend. We get a new polynomial to divide, 0. Then, divide -8 by x² to get -8/x² as the next term of the quotient. Multiply x² - 11x by -8/x and subtract it from the polynomial. Finally, divide 72x by x² to get 72x/x² as the last term of the quotient. Multiply x² - 11x by 72x/x and subtract it from the polynomial. The final quotient is x - 8/x² + 72x/x and the remainder is 0.
Learn more about Long division of polynomials here:
https://brainly.com/question/32236265
#SPJ11
