P(x) is a polynomial of degree 4, and $P (x + 2) - P (x) = x^{3} + 3 x^{2} + x + 1$ , What is the value of P(6), if P(2)=12?

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117

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152

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Solution

The correct option is C
152

Given that $P (x + 2) - P (x) = x^{3} + 3 x^{2} + x + 1 P u t x = 2, \Rightarrow P (4) - P (2) = 2^{3} + 3 \times 2^{2} + 2 + 1 \Rightarrow P (4) - 12 = 8 + 12 + 2 + 1 \Rightarrow P (4) - 12 = 23 \Rightarrow P (4) = 12 + 23 = 35$
Now put $x = 4$ $P (x + 2) - P (x) = x^{3} + 3 x^{2} + x + 1 \Rightarrow P (6) - P (4) = 4^{3} + 3 \times 4^{2} + 4 + 1 \Rightarrow P (6) - 35 = 64 + 48 + 4 + 1 = 117 \Rightarrow P (6) = 117 + 35 = 152$

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P(x) is a polynomial of degree 4, and P(x+2)−P(x)=x3+3x2+x+1, What is the value of P(6), if P(2)=12?

The correct option is C 152Given that P(x+2)−P(x)=x3+3x2+x+1Put x=2,⇒P(4)−P(2)=23+3×22+2+1⇒P(4)−12=8+12+2+1⇒P(4)−12=23⇒P(4)=12+23=35 Now put x=4 P(x+2)−P(x)=x3+3x2+x+1⇒P(6)−P(4)=43+3×42+4+1⇒P(6)−35=64+48+4+1=117⇒P(6)=117+35=152

P(x) is a polynomial of degree 4, and $P (x + 2) - P (x) = x^{3} + 3 x^{2} + x + 1$ , What is the value of P(6), if P(2)=12?