Question

Use synthetic division to tind the quotient an (x³-2x²-12)-:(x+2)

Answer 1

To use synthetic division, set up the synthetic division table with the coefficients of the dividend, divide each coefficient by the divisor, and write the results in the next row. The last entry in the row is the quotient.

Step-by-step explanation:

Synthetic division is a method used to find the quotient of a polynomial division. To use synthetic division, the divisor must be in the form x - a. In this case, the divisor is x + 2. We rewrite the divisor as x - (-2) and set up the synthetic division table with the coefficients of the dividend, which are 1, -2, and -12.

Using synthetic division, we divide each coefficient by the divisor and write the results in the next row. The last entry in the row is the quotient. In this case, the quotient is x^2 - 4x + 8. Therefore, the answer is x^2 - 4x + 8.