Question

when x power 40 +2 is divided by x power 4 +1 , find remainder

Answer 1

Answer:

Given:

• polynomial $x^{40} +2$
• and dividend $x^4+1$

Solving Question:

   We know that if the polynomial p(x) is divided by f(a) then,the remained would be  p(a).

thus , by this method e can find answer .

Solution:

$Given:\: x^{40}+2\\\\\implies (x^4)^{10} + 2.........equ(1)\\\\take\:the\:dividend\\\\ x^4+1=0\\\\\implies x^4=-1............equ(2)\\\\substitute\:the\:value\:equ(2)\:in\:equ(1)\\\\\implies( x^4)^{10}+2\\\\\implies (-1)^{10}+2\\\\\implies 1+2 = 3$

Thus, the remainder is 3