How to solve this question on a quadratic polynomial in a short period of time? The remainders from two divisions are given.

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Answer 1 · 2018-03-18T09:02:58

Answer is (3)

Using remainder theorem we have

$P(1)=4$ and $P(-1)=6$

Further $P(0)=1$ means $P(x)=ax^2+bx+1$

as $P(1)=4$ , $a+b=3$ and as $P(-1)=6$ , $a-b=5$

Hence $a=4$ and $b=-1$

and $P(2)=4*2^2-1*2+1=15$

and $P(-2)=4*(-2)^2-1*(-2)+1=19$

Hence, answer is (3)