Q5 of 64 Page 49

If polynomial p(x) is divided by x2 + 3x + 5, the quotient polynomial and the remainder polynomials are 2x2 + x + 1 and x — 3 respectively. Find p(x).

Here, divisor polynomial s(x) = x2 + 3x + 5


quotient polynomial q(x) = 2x2 + x + 1


remainder polynomial r(x) = x – 3


We know that,


Dividend = Divisor × Quotient + Remainder


∴ p(x) = s(x) × q(x) + r(x)


∴ p(x) = (x2 + 3x + 5) × (2x2 + x + 1) + (x – 3)


∴ p(x) = 2x4 + x3 + x2 + 6x3 + 3x2 + 3x + 10x2 + 5x + 5 + x – 3


∴ p(x) = 2x4 + 7x3 + 14x2 + 9x + 2


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