Question

When dividing (x^3 - 6x^2 - 8x - 19) by (x + 1), what is the quotient?

A) x^2 - 7x + 1
B) x^2 - 7x - 11
C) x^2 - 5x - 11
D) x^2 - 5x + 1

Answer 1

The quotient when dividing (x^3 - 6x^2 - 8x - 19) by (x + 1) using synthetic division is x^2 - 7x + 1, which corresponds to option A.

Step-by-step explanation:

The student is asking to find the quotient when dividing the polynomial (x3 - 6x2 - 8x - 19) by the binomial (x + 1). To solve this, we can use either polynomial long division or synthetic division.

Using synthetic division, we first write the coefficients of the dividend: 1 (for x3), -6 (for -6x2), -8 (for -8x), and -19 (as the constant term). The zero of the divisor, x + 1, is -1. We then perform synthetic division:

1. Bring down the 1.
2. Multiply -1 by 1 and write the result (-1) under -6 and add them to get -7.
3. Multiply -1 by -7 and add the result to -8 to get 1.
4. Multiply -1 by 1 and add the result to -19 to get -20, which is the remainder.

The resulting quotient is therefore x2 - 7x + 1, which corresponds to option A.