Answer: The correct option is A, the remainder is 7.
Step-by-step explanation:
The coefficient of terms in the given synthetic division are 4,6 an -3.
Write the first coefficient as it is in bottom line.
Now multiply 1 by 4 and write the result (i.e., 4) in middle line below the second coefficient.
Now add 6 and 4 and write the result (i.e., 10 ) in bottom row.
Now multiply 1 by 10 and write the result (i.e., 10) in middle line below the third coefficient.
Now add -3 and 10 and write the result (i.e., 7 ) in bottom row.
Now the first two terms shows the coefficient of polynomial and last term show the remainder.
Since the last term is 7 therefore, the remainder is 7.