Question

Use synthetic division to find the quotient and remainder when 2x4+10x3−x2+11x+39 is divided by x+1

Answer 1

To use synthetic division to divide the polynomial 2x^4+10x^3−x^2+11x+39 by x+1, follow these steps: write the coefficients of the polynomial and the divisor, perform synthetic division, and find the quotient and remainder.

Step-by-step explanation:

To use synthetic division to find the quotient and remainder when dividing the polynomial 2x^4+10x^3−x^2+11x+39 by x+1, follow these steps:

1. Write the coefficients of the polynomial in descending order of the powers of x. The polynomial becomes 2 10 -1 11 39.
2. Change the sign of the constant term in the divisor to -1. The divisor becomes -1.
3. Perform synthetic division by dividing each term of the polynomial by the divisor.
4. The quotient is the result of the synthetic division: 2x^3 + 8x^2 + 7x + 18.
5. The remainder is the value at the bottom of the synthetic division: 57.