Question

Two solutions of the polynomial equation are given. Use synthetic division to find any remaining solutions.

x^4+9x^3+5x^2-81x=126; -2,-3

Answer 1

The remaining solutions are -7 and 3.

Explanation:

The synthetic division is shown in the attachment. After dividing the first two found factors from the polynomial, the remaining quadratic is ...

x^2 +4x -21 = 0

Its rational roots will be factors of -21, and the sum of their opposites will be 4. Knowing that 21 = 3·7, we can guess that the remaining roots are -7 and 3. The synthetic division confirms that. (A graph also confirms it.)