Question

2x³ - 2 / x - 5 synthetic division
a) 32
b) 18
c) 10
d) 2

Answer 1

Synthetic division is used to divide a polynomial by a binomial. By following specific steps, we can determine the remainder. We need to perform synthetic division with the given polynomial and binomial to find the correct remainder.

Step-by-step explanation:

Synthetic division is used to divide a polynomial by a binomial of the form (x - k), where k is a constant. The steps to perform synthetic division are as follows:

1. Write the coefficients of the polynomial in descending order.
2. Place the constant term of the binomial divisor outside the division symbol.
3. Bring down the first coefficient of the polynomial.
4. Multiply the constant term of the binomial divisor by the value you brought down and write the product below the next coefficient of the polynomial.
5. Add the result obtained in the previous step to the coefficient below it.
6. Repeat steps 4 and 5 for the remaining coefficients of the polynomial.
7. The last number in the bottom row is the remainder.

By performing synthetic division with the polynomial 2x³ - 2 and the binomial x - 5, we can determine the remainder. The answer choices provided are potential remainder values, and we need to find which one is correct.

To do this, we divide the polynomial by the binomial using synthetic division and check the remainder. The correct answer choice will be the one that matches the remainder obtained from the synthetic division.