Question

Find the remainder when x power4+xcube+2xsquare+x+1 is divided by x+1

Answer 1

$<b>$Answer :

$= > {x}^{4} + {x}^{ 3} + 2 {x}^{2} + x + 1 \: by \: x \: + 1 \\ \\ = > x \: + 1 = 0 \\ \\ = > x = - 1 \\ \\ = > f(x) = {x}^{4} + {x}^{3} + 2 {x}^{2} + x + 1 \\ \\ = > f( - 1) = {( - 1)}^{4} + {( - 1)}^{3} + 2 {( - 1)}^{2} + ( - 1) + 1 \\ \\ = > f( - 1) = 1 - 1 + 2 - 1 + 1 \\ \\ = > f( - 1) = 2$

$\color{brown}\underline\textbf{Hence, remainder = 2. }$

Tysm for the question!

Answer 2

find the remainder of x⁴+x³+2x²+x+1 is exactly divisible by (x+1).

x+1)x⁴+x³+2x²+x+1( x³+2x-1
- x⁴+x³
...........................
0 +2x²+x+1
-2x²+2x
....................
0 -x+1
-x-+
.............
0+2
answers ‘+2' is subtracted from x⁴+x³+2x²+x+1is divided by x+1