9. What must be added to polynomial fi)22x21 so that the resultingpoly

1.	9. What must be added to polynomial fi)22x21 so that the resultingpolynomial is exactly divisible by 2
Answer» P(x) = x^4 + 2x^3 -2x² + x -1 d(x) = x² + 2x -3 We divide p(x) by d(x) & find the quotient q(x) & remainder r(x) P(x) = d(x) * q(x) + r(x) We find that r(x) = (-x +2) Hence, the additive inverse of remainder should be added to p(x), so that p( x) will be exactly divisible by d(x) Additive inverse of -x + 2 = (x-2) Ans

9. What must be added to polynomial fi)22x21 so that the resultingpolynomial is exactly divisible by 2

Answer»

P(x) = x^4 + 2x^3 -2x² + x -1

d(x) = x² + 2x -3

We divide p(x) by d(x) & find the quotient q(x) & remainder r(x)

P(x) = d(x) * q(x) + r(x)

We find that r(x) = (-x +2)

Hence, the additive inverse of remainder should be added to p(x), so that p( x) will be exactly divisible by d(x)

Additive inverse of -x + 2

= (x-2) Ans