(r^3+6r^2-21r-18) ÷ (r-3) show in synthetic division

r² + 9r + 6

Step-by-step explanation:

+3|  +1    +6   -21   -18

   |         +3   +27  +18  

      +1    +9    +6     0

=1r² +9r + 6 + 0

=r² +9r + 6    (simplified)

Read on if you want to know how it was done.

To do synthetic division, you first need to get the constant of the divisor and change the sign.

Then list the coefficients of the dividend.

Drop the first coefficient.

Multiply it by the divisor, and write the answer under the next coefficient and add. Repeat till the end.

The answer should be one degree less, the original polynomial.

For this case we must build a quotient such that when multiplied by the divisor, it eliminates the terms of the dividend until it reaches the remainder.

According to the figure we have that the quotient is:

Quotient:

See attached image

step-by-step explanation: