Resposta final para o problema
Solução explicada passo a passo
Como devo resolver esse problema?
- Escolha uma opção
- Write in simplest form
- Resolva usando fórmula quadrática
- Derive usando a definição
- Simplificar
- Encontre a integral
- Encontre a derivada
- Fatorar
- Fatore completando o quadrado
- Encontre as raízes
- Carregue mais...
We can factor the polynomial $12x^3+13x^2-59x+30$ 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 $30$
Aprenda online a resolver problemas passo a passo.
$1, 2, 3, 5, 6, 10, 15, 30$
Aprenda online a resolver problemas passo a passo. (12x^3+13x^2-59x+30)/(4x-5). We can factor the polynomial 12x^3+13x^2-59x+30 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 30. Next, list all divisors of the leading coefficient a_n, which equals 12. The possible roots \pm\frac{p}{q} of the polynomial 12x^3+13x^2-59x+30 will then be. Trying all possible roots, we found that \frac{5}{4} is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.