Final answer to the problem
Step-by-step Solution
Learn how to solve synthetic division of polynomials problems step by step online. Simplify the expression f(x)=(x^2-3x+2)(3x^3-x^2+4). We can factor the polynomial \left(3x^3-x^2+4\right) using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals 4. Next, list all divisors of the leading coefficient a_n, which equals 3. The possible roots \pm\frac{p}{q} of the polynomial \left(3x^3-x^2+4\right) will then be. Trying all possible roots, we found that -1 is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.
