Question

b) Divide 6x3-X2 +9x + 2 by (2x + 1) and verify the division rule.​

Answer 1

Answer:

your questions is wrong

Answer 2

Dividing $6x^{3}-x^{2} +9x+2$ by 2x + 1 and verifying division rule:

                    2x + 1) $6x^{3}-x^{2} +9x+2$ ($3x^{2} -2x+\frac{11}{2}$

                                 $6x^{3}+3x^{2}$

                             ```````````````````````````````

                                            $-4x^{2} +9x$

                                            $-4x^{2}-2x$

                                         ````````````````````````

                                                         $11x+2$

                                                         $11x+\frac{11}{2}$

                                                     ``````````````````````````````

                                                                  $\frac{-7}{2}$

Verification of division rule:

We know that,

            Dividend = divisor x quotient + remainder

here,  Dividend $=6x^{3}-x^{2} +9x+2$

          Divisor $=2x+1$

          Quotient $=3x^{2} -2x+\frac{11}{2}$

          Remainder = - 7/2

            $6x^{3}-x^{2} +9x+2$ = $(3x^{2} -2x+\frac{11}{2})(2x+1)+(-\frac{7}{2})$

            $6x^{3}-x^{2} +9x+2=6x^{3}-4x^{2} +11x+3x^{2}-2x+\frac{11}{2}-\frac{7}{2}$

            $6x^{3}-x^{2} +9x+2=6x^{3}-x^{2} +9x+2$

             ∴ LHS = RHS

Hence, the division rule for given polynomial is verified.