Question

On dividing p(x) by x^2 + 2x + 2, the quotient and remainder are x^2 + 1 and 18 respectively. find p(x) .

Answer 1

This is the required solution.

Answer 2

Given:-

-»g(x)=x²+2x+2=[Dividend]

-»q(x)=x²+1=[Quotient]

-»r(x)=18=[Remainder]

$\rule{200}{1}$

To Find:-

--›The Polynomial, p(x)?

$\rule{200}{1}$

AnsWer:-

♦Using Euclid's Division Algorithm♦

→p(x)=g(x)×q(x)+r(x)

★Putting The Values★

→p(x)=(x²+2x+2)(x²+1)+18

→p(x)=x⁴+2x³+2x²+x²+2x+2+18

→p(x)=x⁴+2x³+3x²+2x+20

$\rule{200}{2}$