Explain how to find the quotient of: (8a3+31a2-20a-5)/(8a-1)

Answer:

Quotient = a²+ 4a- 2

Step-by-step explanation:

(8a3+31a2-20a-5)/(8a-1)

 =

             a²  +4a-2     ⇒ quotient

(8a-1)√(8a3+31a2-20a-5)

              8a²- a²                  ⇒       Multiplying  (8a-1) by a²

             -     +        ⇒   Changing signs

                     32a²- 20a- 5                

                    32a²- 4a            ⇒   Multiplying  (8a-1) by 4a

                    -        +     ⇒Changing signs

                             -16a -5

                             - 16a +2          ⇒    Multiplying  (8a-1) by -2

                              +       -      ⇒  Changing signs

                                         -7  ⇒ Remainder

We follow the steps of simple division to get the quotient which is a²+ 4a- 2

We multiply  (8a-1) by factors such as a², +4a and -2 to get the same terms as given in the dividend.

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