Question

If P(x) is polynomial of degree $4$ with leading coefficient as three such that $P\left(1\right)=2,P\left(2\right)=8,P\left(3\right)=18,P\left(4\right)=32$, then the value of $P\left(5\right)$ is :

• A. $120$
• B. $121$
• C. $122$
• D. $123$

Answer 1

Answer: (C)

$122$

Let P(x) be $3x^4+b{x}^3+c{x}^2+dx+e$

$P\left(1\right)=2$

$⟹b+c+d+e=-1$

$P\left(2\right)=8$

$⟹8b+4c+2d+e=-40$

$P\left(3\right)=18$

$⟹27b+9c+3d+e=-225$

$P\left(4\right)=32$

$⟹64b+16c+4d+e=-736$

Solving equations, we get, $b=-30,c=107,d=-150,e=72$

Now,

$P\left(5\right)=1875+125b+25c+5d+e$

$⟹P\left(5\right)=1875-30\times 125+25\times 107-5\times 150+72=122$

Thus the answer is $C$