Let P(x)=a₀+a₁ x+a₂ x^2+ .+a_n x^n be a polynomial in which a_i is non-negative integer for each i 0,1,2,3, , n . If P(1)=4 and P(5)=136 , what is the value of P(3) ?

Question

Quantrex Academy · Accepted Answer

Correct answer: 34

aligned & a₀+a₁+a₂+ +a_n=4 & a_i 4 & a₀+5 a₁+5^2 a₂+ .+a 5^n a_n=136 & a₀=1+5 a₀=1 & Hence 5 a₁+5^2 a₂+ .+5^n a_n=135 & a₁+5 a₂+ .5^ n-1 a_ n-1 =27 & a₁=5 +2 a₁=2 & 5 a₂+ 5^ n-1 a_ n-1 =25 & a₂+5 a₃+ . .5^ n-2 a_ n-2 =5 & a₂=5 a₂=0 & a₃+5 a₄+ .+5^ n-3 a_ n-3 =1 & a₃=1 & a₄+5 a₅+ . .+5^ n-4 a_ n-3 =0 & a₄=a₅= . a_n=0 & Hence P(n)=x^3+2 x+1 & P(3)=34 aligned

Let P(x)=a₀+a₁ x+a₂ x^2+ .+a_n x^n be a polynomial in which a_i is non-negative integer for each i 0,1,2,3, , n . If P(1)=4 and P(5)=136 , what is the value of P(3) ?

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