Question

The cubic polynomial $p\left(x\right)$ satisfies $p\left(0\right)=1,p\left(1\right)=20,p\left(2\right)=40,p\left(3\right)=60.$ Then the value of $p\left(4\right)$ is

• A. $78$
• B. $79$
• C. $80$
• D. $81$

Answer 1

The correct option is B $79$

$p\left(x\right)=\lambda (x-1)(x-2)(x-3)+20xp\left(0\right)=1\Rightarrow \lambda =-\frac{1}{6}\therefore p\left(x\right)=-\frac{1}{6}(x-1)(x-2)(x-3)+20x\Rightarrow p\left(4\right)=-1+80=79$