The polynomial is
$$2x^5 + 6x^4 + 7x^3 + 21x^2 + 5x + 15$$
I want to find out the easiest way I can do factorize. Please show me the steps.
2026-02-23 04:56:27.1771822587
How to factorize the quintic polynomial $2x^5 + 6x^4 + 7x^3 + 21x^2 + 5x + 15$?
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By the rational root test we see that $x=-3$ is a root. Using polynomial division, we see that the polynomial factors as $$ (x+3)(x^2+1)(2x^2+5). $$ Alternatively we see that $i$ is a root, hence $x^2+1$ is a factor.