Question

A) what is the remainder obtained by dividing x7+x5+1 by polynomial x3+1

Answer 1

this is answer for ur question

Answer 2

Answer:

$-x^2+x+1$

Step-by-step explanation:

$Dividend =x^7+x^5+1$

$Divisor =x^3+1$

We know that $Dividend = (Divisor \times Quotient) + Remainder$

$x^7+x^5+1= (x^3+1  \times x^4) + (x^5-x^4+1)$

$x^7+x^5+1= (x^3+1  \times x^4+x^2) + (-x^4-x^2+1)$

$x^7+x^5+1= (x^3+1  \times x^4+x^2-x) + (-x^2+x+1)$

So, The remainder is $-x^2+x+1$

Hence he remainder obtained by dividing $x^7+x^5+1$by polynomial $x^3+1$ is $-x^2+x+1$