Step-by-step Solution

Factor the polinomial $x^3+12x^2+21x+10$

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Step-by-step explanation

Problem to solve:

$x^3+12x^2+21x+10$

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$1, 2, 5, 10$

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Learn how to solve polynomial factorization problems step by step online. Factor the polinomial x^3+12x^2+21x+10. We can factor the polynomial x^3+12x^2+21x+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. The possible roots \pm\frac{p}{q} of the polynomial x^3+12x^2+21x+10 will then be. Trying all possible roots, we found that -10 is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.

Final Answer

$\left(x+1\right)^{2}\left(x+10\right)$

Problem Analysis