Final answer:
To find the remaining factors of the polynomial x^3 + x^2 - 10x + 8, one can divide by the given factor x - 2 and then use the quadratic formula to solve the resulting quadratic equation, yielding the remaining factors.
Step-by-step explanation:
The question asks us to find the remaining factors of the polynomial x^3 + x^2 - 10x + 8. Given that x - 2 is a factor, we can use polynomial division or synthetic division to divide the polynomial by this factor. After performing the division, we are left with a quadratic polynomial equation, which can then be solved using the quadratic formula. This will give us the remaining factors of the original polynomial.
To solve for the remaining factors, we first divide the polynomial by x - 2. After division, let's say we receive a quadratic polynomial ax^2 + bx + c. We then apply the quadratic formula, which is x = (-b ± √(b^2 - 4ac))/(2a), to find the solutions for x. These solutions will correspond to the remaining factors in the form of (x - solution1) and (x - solution2).