9.1. Replace the two asterisks with two numbers so that the identity equality is obtained: $(2 x+*)^{3}=5 x^{3}+(3 x+*)\left(x^{2}-x-1\right)-10 x^{2}+10 x$.
Answer: Replace the first asterisk with -1, the second with 1. Solution. Let $a$ be the value of the first asterisk, $b$ be the value of the second. By equating the coefficients of $x^{2}$, $x$, and the constant terms, after combining like terms (and after checking that the coefficients of $x^{3}$ on the right and left sides are the same, equal to 8), we will have the system

$\left\{\begin{array}{l}12 a=-3+b-10 \\ 6 a^{2}=-3-b+10 \\ a^{3}=-b .\end{array}\right.$

Substituting $b=12 a+13$ from the first equation into the second, we get

$6 a^{2}+12 a+6=0$. From this, $a=-1, b=1$, and by verification, we see that the third equation is satisfied for these values.