Question

Find the quotient and remainder when the polynomial 2x³+x+3 is divided by the polynomial x+1

1) quotient =2x²+2x+3, remainder =0.
2) quotient =2x²+2x+3, remainder =6.
3) quotient =2x²−x−1, remainder =4.
4) quotient =2x²−2x+3, remainder =2.

Answer 1

After performing polynomial long division on the polynomial 2x³+x+3 when divided by x+1, the correct quotient is 2x² - x - 1 with a remainder of 4.

The question involves finding the quotient and remainder for the division of the polynomial 2x³+x+3 by x+1. In order to solve this problem, we perform polynomial long division.

The first step is to divide the leading term of the numerator polynomial (2x³) by the leading term of the denominator polynomial (x) to get the first term of the quotient, which is 2x². Next, we multiply the entire denominator by this term and subtract the result from the numerator polynomial, yielding a new, smaller polynomial.

Continuing this process until the degree of the polynomial in the remainder is less than the degree of the denominator polynomial, we obtain the final quotient and remainder. After performing long division, the correct option is quotient = 2x² - x - 1, remainder = 4.

Therefore, the correct answer to the question is option 3.