Let
![p(x)](/media/m/3/9/3/393afccb4b82415d2114a3ff957b444f.png)
be a cubic polynomial with integer coefficients with leading coefficient
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
and with one of its roots equal to the product of the other two. Show that
![2p(-1)](/media/m/2/3/6/2362787ec2252a951cc41aa15f5a4bff.png)
is a multiple of
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Let $p(x)$ be a cubic polynomial with integer coefficients with leading coefficient $1$ and with one of its roots equal to the product of the other two. Show that $2p(-1)$ is a multiple of $p(1)+p(-1)-2(1+p(0)).$