Question

Use synthetic division to find the result when x³+7x²+7x-6 is divide by x+2.

Answer 1

Synthetic division of x³+7x²+7x-6 by x+2 results in x²+5x-3, with a remainder of 0, indicating that x+2 is a factor of the polynomial.

Step-by-step explanation:

To find the result whenb using synthetic division, we follow these steps:

1. Identify the coefficient of the divisor, which is -2 for the divisor x+2.
2. Write down the coefficients of the polynomial to be divided, which are 1, 7, 7, and -6 for x³+7x²+7x-6.
3. Perform synthetic division by bringing down the leading coefficient, 1, and then follow the process of multiply by -2, add, repeat.
4. The synthetic division should look like this:

-2 | 1 7 7 -6
| -2 -10 6
----------------
1 5 -3 0

The remainder is 0, so x+2 is a factor of the polynomial. The result of the division is x²+5x-3.

Always remember to eliminate terms wherever possible to simplify the algebra, and check the answer to see if it is reasonable.