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Question

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

A
120
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B
121
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C
122
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D
123
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Solution

The correct option is B 122
Let P(x) be 3x4+bx3+cx2+dx+e
P(1)=2
b+c+d+e=1
P(2)=8
8b+4c+2d+e=40
P(3)=18
27b+9c+3d+e=225
P(4)=32
64b+16c+4d+e=736
Solving equations, we get, b=30, c=107, d=150, e=72
Now,
P(5)=1875+125b+25c+5d+e
P(5)=187530×125+25×1075×150+72=122
Thus the answer is C

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