SAT Question f237ccfc: Equivalent Expressions answer and explanation with Desmos solution

The sum of the given expressions is $(-2x^2+x+31)+(3x^2+7x-8)$. Combining like terms yields $x^2+8x+23$. Based on the form of the given equation, $a=1$, $b=8$, and $c=23$. Therefore, $a+b+c=32$. Alternate approach: Because $a+b+c$ is the value of $a{x}^2+bx+c$ when $x=1$, it is possible to first make that substitution into each polynomial before adding them. When $x=1$, the first polynomial is equal to $-2+1+31=30$ and the second polynomial is equal to $3+7-8=2$. The sum of $30$ and $2$ is $32$.