ข้อสอบคณิต O-NET - 2554

$$\begin{gathered} \mathrm{จากโจทย์} \\ {\left(x-1\right)}^2\left(ax+b\right) = c{x}^3+dx+4 \\ \mathrm{จะได้} \left(x^2-2x+1\right)\left(ax+b\right) = c{x}^3+dx+4 \\ a{x}^3+b{x}^2-2a{x}^2-2bx+ax+b = c{x}^3+dx+4 \\ a{x}^3+\left(b-2a\right)x^2+\left(-2b+a\right)x+b = c{x}^3+dx+4 \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้} b-2a = 0 \dots \overline{)1} \\ -2b+a = d \dots \overline{)2} \\ b = 4 \dots \overline{)3} \end{gathered}$$

$$\begin{gathered} \mathrm{แทน} \overline{)3} \mathrm{ใน} \overline{)1} ; 4-2a = 0 \\ a = 2 \\ \mathrm{แทน} a=2 \mathrm{ใน} \overline{)1} ; b-2\left(2\right) = 0 \\ b = 4 \\ \mathrm{แทน} b=4 \mathrm{ใน} \overline{)2} ; -2\left(4\right)+2 = d \\ d = -6 \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้} a+b+c+d = 2+4+2+\left(-6\right) \\ = 2 \\ \mathrm{ดังนั้น} \mathrm{ตอบ} 2 \end{gathered}$$