Final answer:
The problem involves simplifying a polynomial expression by performing polynomial division. This requires dividing the higher-degree polynomials in the numerator by the linear polynomial in the denominator, similar to long division.
Step-by-step explanation:
The question asks us to simplify the equation (-x4+20x2-19x+12)/(x-4). To tackle this problem, we need to perform polynomial division, where we divide the numerator by the denominator. This process is similar to long division but with polynomials instead of numbers. Since this is not a simple factorable expression, we need to use the polynomial division technique step by step, or we could also apply synthetic division if we recognize that one of the roots of the polynomial might be the value of x for which the denominator equals zero (in this case, x = 4).
Once we go through the division process, we will obtain a simplified form of the polynomial, which should be a polynomial of a degree less than the original, since we are dividing by a linear term (x-4).
To perform polynomial division, we look at the highest degree terms first, divide them, and subtract the result from the original polynomial. We repeat the process with the new polynomial obtained until we reach a degree that's less than that of the divisor, which may also result in a remainder.