Question

Divide the first polynomial by the second. State the quotient and the remainder. x^(3)-5x^(2)-10x+24,x-6 The quotient is with a remainder of

Answer 1

To divide polynomials using long division, we divide the terms one by one and subtract the products from the dividend. For this problem, the quotient is x - 6 and the remainder is 4x + 48.

Step-by-step explanation:

To divide polynomials, we can use long division. In this case, we will divide x⁴ - 5x⁵ - 10x + 24 by x - 6.
First, write the dividend and the divisor, making sure the terms are arranged in descending order of exponents.

Divide the first term of the dividend (x⁴) by the first term of the divisor (x).Multiply the quotient (x) by the divisor (x - 6), and write the product below the dividend.Subtract the product from the dividend, and bring down the next term (- 5x).Repeat the process until all terms have been divided.

The quotient is x - 6, and the remainder is 4x + 48.