Question

Find the product of uncommon real roots of the two polynomials $P(x)=x^4+2x^3-8x^2-6x+15$ and $O(x)=x^3+4x^2-x-10$

Answer 1

Answer: 6

$x=-2$ is a root of the second polynomial $Q(x)$. So $Q(x)=(x+2)\left(x^2+2x-5\right)$ $x=-2$ is not a root of the first polynomial $P(x)$.
Then check if $\left(x^2+2x-5\right)$ is the root of $P(x)$. $P(x)=\left(x^2-3\right)\left(x^2+2x-5\right)$. So the product of uncommon real roots is $(-3)(-2)=6$