OpenSAT

If $x-2$ is a factor of $2x^2 + ax + b$, then the polynomial must equal 0 when $x = 2$. Substituting 2 for $x$ in the expression, we get $2(2)^2 + a(2) + b = 0$. Simplifying, we have $8 + 2a + b = 0$. Since the coefficient of $x^2$ is 2, the coefficient of the constant term $b$ must also be 2 times the constant term in the factored form $(x - 2)$. This means that $b = -8$, which is the constant term in the factored form, $2(x-2)(x+2) = 0$. Substituting $b = -8$ into the equation $8 + 2a + b = 0$ gives $8 + 2a - 8 = 0$, or $2a = 0$, so $a = 0$. Therefore, the value of $b$ is -8.