<s>[INST] Why does $3x^4 + 16x^3 + 20x^2 - 9x - 18$ = $(x+3)(x+2)(\frac{-1 \mp \sqrt 37 }{6})3$? $$3x^4 + 16x^3 + 20x^2 - 9x - 18 $$
When simplified I arrive to:
$$ (x+3)(x+2)(\frac{-1 \mp \sqrt 37 }{6}) $$
But the math book wrote:
$$ (x+3)(x+2)(\frac{-1 \mp \sqrt 37 }{6})3 $$
with that extra 3 at the end. The graph calculator seem to agree with that extra 3 as well. what did I do wrong?
 [/INST] By the rational root test the polynomial has the two roots $x=-2$ and $x=-3$ so that
$$
3x^4 + 16x^3 + 20x^2 - 9x - 18=(x+2)(x+3)(3x^2+x-3)
$$
The extra $3$ is not an exponent but is the leading coefficient in $3x^2+x-3$.
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