Question

What should be subtracted from the polynomial x + 2x + 8x +22x + 18 so that it is completely divisible
by x2 + 6 ?​

Answer 1

$\text{I think your question is }$

$\text{What should be subtracted from the polynomial x^4+2x^3+8x^2+22x +18 }$

$\text{so that it is completely divisible by x^2 + 6 ?}$

$\text{First we find the remainder when }x^4+2x^3+8x^2+22x +18$ $\text{ is divided by x^2 + 6 using long division method}$

$\begin{array}{r|l}&x^2+2x+2\\\cline{2-2}\\x^2+0x+2&x^4+2x^3+8x^2+22x+18\\&x^4+0x^3+6x^2\\\cline{2-2}&\;\;\;\;\;\;\;2x^3+2x^2+22x\\&\;\;\;\;\;\;\;2x^3+0x^2+12x\\\cline{2-2}&\;\;\;\;\;\;\;\;\;\;\;\;\;2x^2+10x+18\\&\;\;\;\;\;\;\;\;\;\;\;\;\;2x^2+0x+12\\\cline{2-2}&\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;10x+6\\\cline{2-2}\end{array}$

$\text{The remainder we obtain from long division is 10x+6}$

$\therefore\text{10x+6 should be subtracted from}$ $x^4+2x^3+8x^2+22x +18$ $\text{so that it is completely divisible by}x^2 + 6$

Find more:

By using long division method show that x minus 3 is a factor of 6 + X - 4 x square + x cube​

https://brainly.in/question/14713178#

Answer 2

Answer:

I think your question is

What should be subtracted from the polynomial x4+2x3+8x2+22x+18\text{What should be subtracted from the polynomial $x^4+2x^3+8x^2+22x +18$}What should be subtracted from the polynomial x

4

+2x

3

+8x

2

+22x+18

so that it is completely divisible by ?x2+6\text{so that it is completely divisible by $x^2 + 6$?}so that it is completely divisible by x

2

+6?

First we find the remainder when x4+2x3+8x2+22x+18\text{First we find the remainder when }x^4+2x^3+8x^2+22x +18First we find the remainder when x

4

+2x

3

+8x

2

+22x+18 is divided by using long division methodx2+6\text{ is divided by $x^2 + 6$ using long division method} is divided by x

2

+6 using long division method

The remainder we obtain from long division is 10x+6\text{The remainder we obtain from long division is 10x+6}The remainder we obtain from long division is 10x+6

∴10x+6 should be subtracted from\therefore\text{10x+6 should be subtracted from}∴10x+6 should be subtracted from x4+2x3+8x2+22x+18x^4+2x^3+8x^2+22x +18x

4

+2x

3

+8x

2

+22x+18 so that it is completely divisible byx2+6\text{so that it is completely divisible by}x^2 + 6so that it is completely divisible byx

2

+6