A2 Polynomials $p$ and $q$ with the formulas $p(x)=-2 x^{2}+1-3 x$ and $q(x)=a\left(2-x^{2}\right)+b+c(2-x)$ are equal if:
(A) $a=4, b=1, c=3$
(B) $a=2, b=9, c=3$
(C) $a=2, b=-9, c=3$
(D) $a=-4, b=1, c=3$
(E) $a=-2, b=9, c=-3$
A2. We arrange the polynomial $q$: $q(x)=2a-ax^2+b+2c-cx=-ax^2-cx+2a+b+2c$. We equate the coefficients of the polynomials $-2=-a, -3=-c$ and $1=2a+b+2c$. We calculate $a=2, c=3$ and $2 \cdot 2+b+2 \cdot 3=1$, from which we calculate $b=-9$.