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Rewrite the expression $\frac{3x^3-x^2+2x-4}{x^2-3x+2}$ inside the integral in factored form
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$\int_{0}^{2}\frac{3x^3-x^2+2x-4}{\left(x-1\right)\left(x-2\right)}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (3x^3-x^22x+-4)/(x^2-3x+2) from 0 to 2. Rewrite the expression \frac{3x^3-x^2+2x-4}{x^2-3x+2} inside the integral in factored form. We can factor the polynomial 3x^3-x^2+2x-4 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 3x^3-x^2+2x-4 will then be.