Question

(8x⁴+10x³-5x²-4x+1)by(2x²+x-1)

Answer 1

GIVEN :

Divide the polynomial (8x⁴+10x³-5x²-4x+1) by the polynomial (2x²+x-1)

TO FIND :

The remainder and quotient for the given polynomial.

SOLUTION :

Given that divide the polynomial (8x⁴+10x³-5x²-4x+1) by the polynomial (2x²+x-1)

                   $4x^2+3x-2$

             ____________________

2x²+x-1 ) 8x⁴+10x³-5x²-4x+1

             $8x^4+4x^3-4x^2$

          _(-)__(-)___(+)__________

                   $6x^3-x^2-4x$

                   $6x^3+3x^2-3x$

                 _(-)__(-)__(+)______

                          $-4x^2-x+1$

                          $-4x^2-2x+2$

                        _(+)__(+)__(-)__

                                        x-1

                       _____________

The quotient is $4x^2+3x-2$ and remainder is x-1 when the given polynomial (8x⁴+10x³-5x²-4x+1) is divided by the polynomial (2x²+x-1).

∴ The quotient is $4x^2+3x-2$ and remainder is x-1.

Answer 2

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