Learn how to solve differential equations problems step by step online. Find the limit of (x^3-x^2-x+10)/(x^2+3x+2) as x approaches -2. Factor the trinomial x^2+3x+2 finding two numbers that multiply to form 2 and added form 3. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. We can factor the polynomial x^3-x^2-x+10 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 10. Next, list all divisors of the leading coefficient a_n, which equals 1.

Find the limit of (x^3-x^2-x+10)/(x^2+3x+2) as x approaches -2