Answer :
Final answer:
To divide the polynomial x^3 - 6x^2 + 12x - 48 by x - 3, use polynomial long division by dividing the first terms, subtracting the product from the dividend, and repeating the process until you have a quotient and a remainder.
Explanation:
To divide the polynomial x^3 - 6x^2 + 12x - 48 by x - 3, we can use polynomial long division or synthetic division. Let's apply the long division method step by step:
- Divide the first term of the dividend (x^3) by the first term of the divisor (x), which gives us x^2. Write this as the first term of the quotient.
- Multiply the entire divisor by x^2 and subtract the result from the dividend. Simplify what remains.
- Repeat this process with the new dividend, which is the result of the subtraction.
- Continue until the degree of the remainder is less than the degree of the divisor or the remainder is zero.
The result will be a quotient polynomial plus a remainder, if any.
