Question

find value of a and b so that x⁴+x³+8x²+ ax-b is divisible by x²+1 . solve using long divison method.

Answer 1

hope this will help you

Answer 2

GIVEN :

The expression is   is divisible by

TO FIND :

The values of a and b by solving the given polynomials by Long Division method

SOLUTION :

Now divide the given polynomial

$x^4+x^3+8x^2+ax-b$ is divisible by $x^2+1$

$x^2+1$ can be written as $x^2+0x+1$

                                  $x^2+x+7$

                          ______________________

       $x^2+0x+1$ ) $x^4+x^3+8x^2+ax-b$

                            $x^4+0x^3+x^2$

                    ___(-)___(-)__(-)_____________

                                $x^3+7x^2+ax$

                                $x^3+0x^2+x$

                             __(-)__(-)__(-)_____

                                         $7x^2+(a-1)x-b$

                                         $7x^2+0x+7$

                                      _(-)___(-)__(-)___

                                                  (a-1)x-b-7

                                                _________

The quotient is  and remainder is  (a-1)x-b-7

Since the the polynomial is completely divided by  so that the remainder is zero

∴ (a-1)x-b-7=0  

(a-1)x-b-7=0  can be written as

(a-1)x+(-b-7)=0x+0

Now equating the coefficients of x and constant we get

a-1=0 and -b-7=0

∴ a=1 and b=-7

∴ The values of a and b is 1 and -7 respectively.