1. ## Quotient

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

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

Thank you

2. Originally Posted by mj.alawami
Q) $
\frac{6a^2+5a-6}{3a-2}
$

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

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

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

4. 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

5. 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 ?

6. Originally Posted by mj.alawami
How did you factorise so easily the second one ?
He did it using long division.

7. 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?