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Question

Find the quotient of 6x^3-24x^2-9x/3x three different ways:

1. By Factoring

By using Long Division

 By using the Distributive Property

Answer 1

Factoring:

6x³ - 24x² - 9x = 3x(2x² - 8x - 3) so when we divide by 3x, we have 3x/3x which is 1 so the answer is 2x² - 8x - 3

Long Division:

First divide 3x into 6x³. It goes 2x² times because 3x times 2x² equals 6x³. Put the 2x2 up on top and multiply 3x and 2x² to get 6x³ and place it under the other 6x³ and subtract (you get zero). Then bring down the -24x². 3x divided into -24x² goes -8x times because 3x time -8x equals -24x². Put the -8x up on top and multiply 3x and -8x to get -24x². Place the -24x² under the other -24x² and subtract. That makes the bottom one a positive and when you add you get zero. Then bring down the -9x and continue.

The distributive property:

Divide each part of the numerator by the "3x" denominator.

The result is 2x² - 8x - 3

Answer 2

Lets start with factoring, since that is a bit easier. In the expression 6x³-24x²-9x, all terms share a common denominator of 3, which can be pulled out of the expression as follows...

3(2x³-8x²-3x) --> I just divided the coefficients of all the terms by 3

All the terms all have a common factor of x, so when it is factored out, it looks like this...

3x(2x²-8x-3)

Therefore, your quotient is 2x²-8x-3

For long division, you just divide each of the terms individually by 3x.

6x³/3x = 2x² (no remainder)

-24x²/3x = -8x (no remainder)

-9x/3x = -3 (no remainder)

When you add all these up, you get 2x²-8x-3