What is the remainder in the synthetic division problem below?

The remainder is 25  ⇒ answer (C)

Step-by-step explanation:

* The remainder will be the last number in the calculation

* From the picture the dividend is 3x³ + x² + 2x - 7 and x - 2 is the divisor

- In the synthetic calculation we use the coefficient of the dividend with the value of x when the divisor = 0

- From the picture the divisor is x - 2, when x - 2 = 0, then x = 2

∵ The coefficient of the dividend are 3 , 1 , 2 , -7

Step 1 : Write down the coefficients of the dividend , put x = 2 at the left  

                         2        3    1    2    -7    

Step 2 : Bring down the first coefficient to the bottom row.

                         2        3    1    2    -7    

                                    3

Step 3 : Multiply it by 2, and carry the result into the next column.

                       2        3    1    2    -7    

                                 ___6

                                  3

Step 4 : Add down the column

                       2        3    1    2    -7    

                                 ___6

                                 3     7

Step 5 : Multiply it by 2, and carry the result into the next column

                       2        3    1    2    -7  

                                 ___6_14

                                 3     7

Step 6 : Add down the column

                       2        3    1    2    -7    

                                 ___6_14

                                 3     7   16

Step 7 : Multiply it by 2, and carry the result into the next column

                     2        3    1    2    -7    

                               ___6_14_32

                               3     7  16

Step 8 : Add down the column

                  2        3    1    2    -7    

                            ___6_14_32

                             3   7  16   25

∴ The quotient is (3x² + 7x + 16) and the remainder is 25

the statemwnt is the company makes small and large snow cone cups.

large=it holds more then the small

small=it holds less then the large

answer: a.   one is a factor of every whole number since every number is divisible by itself.