Question

What is the result when 2x^3 - 8x^2 + 11x - 5 is divided by x - 1?

Answer 1

To find the result of dividing the polynomial 2x^3 - 8x^2 + 11x - 5 by x - 1, one can use synthetic division, which involves a series of multiplications and additions to determine the coefficients of the quotient polynomial.

Step-by-step explanation:

The result when 2x^3 - 8x^2 + 11x - 5 is divided by x - 1 can be found using polynomial long division or synthetic division. To use synthetic division, we replace 'x' with 1 and find the coefficients for the quotient:

1. Write down the coefficients of 2x^3, -8x^2, 11x, and -5.
2. Bring down the leading coefficient (2).
3. Multiply the divisor root (1) by the first coefficient (2) and write the result under the second coefficient (-8).
4. Add the second coefficient (-8) and the multiplication result (2) to find the new coefficient and continue this process for each term.
5. The new set of numbers represents the coefficients of the quotient polynomial.

By performing these steps, we can determine the quotient of the division.