You can use long division of polynomials. To start set up the problem in long division format, with the denominator out in front and the numerator under the division sign.
color(white)(x/color(black)(x+3)) ()/(")" x^3 +0x^2 + 0x + 27)
To start the division, look at the first term of each term. What do you need to multiply x by to get x^3? The answer is x^2, so that goes on the top.
color(white)(x/color(black)(x+3)) (x^2color(white)(-3x -9 +27x))/(")" x^3 +0x^2 + 0x + 27)
Now multiply the divisor, x+3, by x^2 and subtract from the dividend. Remember, subtraction happens in columns.
color(white)(x/color(black)(x+3)) (x^2 color(white)(-3x -9 +27x))/(")" x^3 +0x^2 + 0x + 27)
color(white)(XXXx)(x^3 + 3x^2)/(color(white)(x^3)-3x^2)
Now we need to know what to multiply x by to get -3x^2. Its -3x. Write -3x on top, multiply by x+3 and subtract.
color(white)(x/color(black)(x+3)) (x^2-3x color(white)(+9 +27x))/(")" x^3 +0x^2 + 0x + 27)
color(white)(XXXx)(x^3 + 3x^2)/(color(white)(x^3)-3x^2)
color(white)(XXXXX|)(-3x^2-9x)/(color(white)(-3x^2-)9x
Last one, we multiply x by 9 to get 9x.
color(white)(x/color(black)(x+3)) (x^2-3x +9 color(white)(+27x))/(")" x^3 +0x^2 + 0x + 27)
color(white)(XXXx)(x^3 + 3x^2)/(color(white)(x^3)-3x^2)
color(white)(XXXXX|)(-3x^2-9x)/(color(white)(-3x^2-)9x
color(white)(XXXXXXXXXx)(9x+27)/(color(white)(9x+)0)
There is no remainder, so the quotient is;
x^2-3x+9
