Answer:
To divide using long division, we first divide the leading term of the dividend (3r³) by the leading term of the divisor (r) to get the first term of the quotient (3r²). Then, we multiply the divisor (r + 4) by the quotient term (3r²) and subtract it from the dividend. We then bring down the next term of the dividend (11r²) and repeat the process. This will give us the quotient and the remainder.
The long division process is as follows:
(r + 4) | (3r³ +11r²-6r-18)
| 3r² (3r²)
|__
| -9r² +11r²-6r-18
|____
| -2r-18
|____
| +12r + 72
|____
| -36
|____
So the quotient is 3r² - 2r + 12 and the remainder is -36
And we can write the division as (3r³ +11r²-6r-18)÷(r + 4) = 3r² - 2r + 12 +(-36)/(r + 4)