Question

if p(x) is divided by q(x),then the remainder is
p(x):x^5+x^4+x^3+x^2+2x+2
q(x):x^3+1

Options are
2x-1
2x+1
x+1
x-1​

Answer 1

Step-by-step explanation:

A polynomial p(x) is defined as

⇒p(x)=g(x)q(x)+r(x)

where g(x)= divisor ; q(x)= quotient and r(x)= remainder

∴ p(x) can be found by multiplying g(x) with q(x) & adding r(x) to the product.

(i).g(x)=(x−2); q(x)=x2−x+1; r(x)=4

∴p(x)=(x−2)[x2−x+1]+4

              =x3−x2+x−2x2+2x−2+4

              =x3−3x2+3x+2

(ii).g(x)=(x+3); q(x)=2x2+x+5; r(x)=3x+1

∴p(x)=(x+3)[2x2+x+5]+(3x+1)

              =2x3+x2+5x