Question

Find all solutions of the equation.
x^4 + 3x^3 − 13x^2 − 9x + 30 = 0

Answer 1

the Rational Root Theorem shows that the roots are among
±1,±2,±3,±5,±6,±10,±15,±30
A little synthetic division shows that
x^4 + 3x^3 − 13x^2 − 9x + 30 = (x-2)(x^3+5x^2-3x-15)
A little inspection via grouping gives you
(x-2)(x+5)(x^2-3)
so, ...

Answer 2

Try x = 2
16+24-52-18+30 = 0 :) so (x-2) is a factor
or if all else fails
https://www.mathportal.org/calculators/polynomials-solvers/polynomial-factoring-calculator.php
(x-2)(x^2-3)(x+5)
2 , +sqrt 3 , -sqrt 3 , -5