Quotient

**mj.alawami** · February 10th 2009, 11:09 AM

Q) $<br /> \frac{6a^2+5a-6}{3a-2}<br />$
Q) $\frac{5b^3+7b^2+12}{b+2}$

Please answer the following in steps..
Thank you

**topher0805** · February 10th 2009, 11:24 AM

Originally Posted by mj.alawami

Q) $<br /> \frac{6a^2+5a-6}{3a-2}<br />$
Q) $\frac{5b^3+7b^2+12}{b+2}$

Please answer the following in steps..
Thank you

To simplify, start by factoring the numerator:

$6a^2+5a-6 = (3a-2)(2a+3)$

Which gives us:

$\frac{(3a-2)(2a+3)}{(3a-2)}$

Cancel out the common term:

$2a+3$

--------------------------------------------------------

For the 2nd question, you can use long division. I'm not sure about the LaTeX, but it works the same as long division with integers.

If you need to see it, this is a good tutorial: http://www.purplemath.com/modules/polydiv2.htm

**Soroban** · February 10th 2009, 11:30 AM

Hello, mj.alawami!

Just factor and reduce . . .

$\frac{6a^2+5a-6}{3a-2}$

Factor: . $\frac{(2a+3)(3a-2)}{3a-2}$

. . and reduce: . $\frac{(2a+3)({\color{red}\rlap{//////}}3a-2)}{{\color{red}\rlap{//////}}3a-2} \;=\;2a+3$

$\frac{5b^3+7b^2+12}{b+2}$

Factor: . $\frac{(b+2)(5b^2-3b+6)}{b+2}$

. . and reduce: . $\frac{({\color{red}\rlap{////}}b+2)(5b^2-3b+6)}{{\color{red}\rlap{////}}b+2} \;=\;5b^2-3b+6$

**mj.alawami** · February 10th 2009, 12:07 PM

Originally Posted by topher0805

To simplify, start by factoring the numerator:

$6a^2+5a-6 = (3a-2)(2a+3)$

Which gives us:

$\frac{(3a-2)(2a+3)}{(3a-2)}$

Cancel out the common term:

$2a+3$

--------------------------------------------------------

For the 2nd question, you can use long division. I'm not sure about the LaTeX, but it works the same as long division with integers.

If you need to see it, this is a good tutorial: Polynomial Long Division

The long division is very hard and i am getting confused in doing the second one so please tell me how to do it using the long division

**mj.alawami** · February 10th 2009, 12:08 PM

Originally Posted by Soroban

Hello, mj.alawami!

Just factor and reduce . . .

Factor: . $\frac{(2a+3)(3a-2)}{3a-2}$

. . and reduce: . $\frac{(2a+3)({\color{red}\rlap{//////}}3a-2)}{{\color{red}\rlap{//////}}3a-2} \;=\;2a+3$

Factor: . $\frac{(b+2)(5b^2-3b+6)}{b+2}$

. . and reduce: . $\frac{({\color{red}\rlap{////}}b+2)(5b^2-3b+6)}{{\color{red}\rlap{////}}b+2} \;=\;5b^2-3b+6$

How did you factorise so easily the second one ?

**topher0805** · February 10th 2009, 12:16 PM

Originally Posted by mj.alawami

How did you factorise so easily the second one ?

He did it using long division.

**mj.alawami** · February 10th 2009, 12:19 PM

Originally Posted by topher0805

He did it using long division.

Please show me the steps because i am desperate, i can't figure out what to do in the middle of the division

Sorry i got it?

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