Question

Divide using polynomial long division. (2x3 – 16x² + 37x – 26) = (x - 5)

Answer 1

the solution to the given synthetic division will be expressed as $(2x^2 - 6x + 7) + \frac{9}{x-5}$

Synthetic division of a polynomial

According to the given question, we are to divide (2x³ – 16x² + 37x – 26)  by (x - 5)

         2x^2 - 6x + 7

x - 5 | 2x³– 16x² + 37x – 26

          2x³ - 10x²

     __________

                 -6x² +37x

                 -6x² +30x

             _______________

                             7x   - 26

                             7x   - 35
                         ______________

                                       9 - Remainder

Hence the solution to the given synthetic division will be expressed as:

 $P(x) = Q(x) + \frac{R(x)}{D(x)} \\(2x^3 -16x^2 + 37x - 26 = (2x^2 - 6x + 7) + \frac{9}{x-5}$

Learn more on synthetic division here: brainly.com/question/24662212