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)xx+3)x3+0x2+0x+27
To start the division, look at the first term of each term. What do you need to multiply xx by to get x^3x3? The answer is x^2x2, 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)xx+3x2−3x−9+27x)x3+0x2+0x+27
Now multiply the divisor, x+3x+3, by x^2x2 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)xx+3x2−3x−9+27x)x3+0x2+0x+27
color(white)(XXXx)(x^3 + 3x^2)/(color(white)(x^3)-3x^2)XXXxx3+3x2x3−3x2
Now we need to know what to multiply xx by to get -3x^2−3x2. Its -3x−3x. Write -3x−3x on top, multiply by x+3x+3 and subtract.
color(white)(x/color(black)(x+3)) (x^2-3x color(white)(+9 +27x))/(")" x^3 +0x^2 + 0x + 27)xx+3x2−3x+9+27x)x3+0x2+0x+27
color(white)(XXXx)(x^3 + 3x^2)/(color(white)(x^3)-3x^2)XXXxx3+3x2x3−3x2
color(white)(XXXXX|)(-3x^2-9x)/(color(white)(-3x^2-)9xXXXXX∣−3x2−9x−3x2−9x
Last one, we multiply xx by 99 to get 9x9x.
color(white)(x/color(black)(x+3)) (x^2-3x +9 color(white)(+27x))/(")" x^3 +0x^2 + 0x + 27)xx+3x2−3x+9+27x)x3+0x2+0x+27
color(white)(XXXx)(x^3 + 3x^2)/(color(white)(x^3)-3x^2)XXXxx3+3x2x3−3x2
color(white)(XXXXX|)(-3x^2-9x)/(color(white)(-3x^2-)9xXXXXX∣−3x2−9x−3x2−9x
color(white)(XXXXXXXXXx)(9x+27)/(color(white)(9x+)0)XXXXXXXXXx9x+279x+0
There is no remainder, so the quotient is;
x^2-3x+9x2−3x+9
