Question

Find the quotient and remainder when dividing 3x⁴ + 2x² - 6x + 1 by x + 1.

A) 3x³ - x² - 7x + 8
B) 3x³ - x² - 7x
C) 3x³ - x² - 7x + 1
D) 3x³ - x² - 7x - 1

Answer 1

To find the quotient of 3x⁴ + 2x² - 6x + 1 divided by x + 1, perform polynomial long division. The quotient is 3x³ - x² - 7x + 8, making the correct option A) 3x³ - x² - 7x + 8.

Step-by-step explanation:

To find the quotient and remainder when dividing 3x⁴ + 2x² - 6x + 1 by x + 1, we will use polynomial long division. The process is similar to long division of numbers. Below are the steps you need to follow:

1. Divide the first term of the numerator, 3x⁴, by the first term of the denominator, x, to get 3x³.
2. Multiply x + 1 by 3x³ to get 3x⁴ + 3x³ and subtract this from the original polynomial.
3. Bring down the next term (2x²) to get -3x³ + 2x². Divide by x to get -x² and repeat the process.
4. Continue this process until the degree of the remainder is less than the degree of the divisor, x + 1.

When you complete the division, you should find that the quotient is 3x³ - x² - 7x + 8 and the remainder is -7, which indicates that the correct option is A) 3x³ - x² - 7x + 8.