Solve. (-18x^3+17x+6)/(3x+2) Please help! If you can, leave an explanation for the answer! Thanks!

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Solve. (-18x^3+17x+6)/(3x+2) Please help! If you can, leave an explanation for the answer! Thanks!

Mathematics
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long division 5 steps) \(\huge\color{green}{{1:}}\) Divide the first terms \(\huge\color{green}{{2:}}\) multiply(distribute) \(\huge\color{green}{{3:}}\) subtract all terms \(\huge\color{green}{{4:}}\) carry down \(\huge\color{green}{{5:}}\) repeat |dw:1433974939206:dw|there isn't x^2 term in the question but we have to write it in order 3 2 1 0 like this
I believe the problem is "simplify" instead of "solve"
divide first terms \[\rm \frac{ -18x^3 }{ 3x } = ??\]

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=-6x^3? @Nnesha
x^3 can be written as x times x times x so \[\rm \frac{ x \times x \times x }{ x } = ??\]
x^3? @Nnesha
nope you can cancel one x right ?
\[\rm \frac{ x \times x \times \cancel x }{ \cancel x } = ??\]
Ok! So x^2? @Nnesha
yes right!
now 2nd step |dw:1433975352357:dw| distribute divisor by -6x^2 so -6x^2 (3x+2)
So -18x^2 +4? @Nnesha
nope when you multiply same bases you should add their exponents
I understand. So 18x^3+4 @Nnesha
distribute meaning multiply everything which is inside the parentheses by outside term so -6x^2 (3x+2) -6x^2 times 3x = ?? -6x^2 times 2 =?
yes x^3 is right but there is a little mistake :-)
So 18x^3 and 12x^2? @Nnesha
you forgot negative sign
Oh yeah! So -18x^3 and -12x^2? @Nnesha
there you go!
|dw:1433975913009:dw| step 3 change sign and then combine like terms :-)
So 12x^2+17x+6? @Nnesha
yes right! now repeat!
|dw:1433976142678:dw| divide first terms 12x^2/3x
Ok so 4x? @Nnesha
yep!
And the next step is to divide 6 by 2? So would the answer be -6x^2+4x+3? @Nnesha
6 by 2 ??
4x right now 2nd step distribute!
Sorry, I'm confused with what to do next. @Nnesha
1st step is divide you did that now 2nd step distribute 4x by divisor
ok so do I divide 17x by 4x now? @Nnesha
alright nope you don't have to divide by quotient |dw:1433976642990:dw| divide first terms remember 3x stay same
you got 4x now distribute divisor by 4x 4x(3x+2) = ?
|dw:1433976698488:dw|
So 12x+8x? @Nnesha
remember when you multiply same bases you should add their exponents so 4x times 3x = ?
12x^2 @Nnesha
yep right :-)
|dw:1433976885337:dw| try!
Ok so -6x^2+4x+3? @Nnesha
is that the quotient ?
I think so @Nnesha
Is that the correct answer? @Nnesha
is that a guess ?
No, because I distributed 4x and I got 12x^2+8x+6 (I just left the 6 by itself) and then I divided that by 2 to simplify the answer. :) @Nnesha
alright |dw:1433977488813:dw| yes that's right 9x/3x = 3
Ok is that all I had to do for that question? @Nnesha
that's just quotient what is the remainder answer should be like this \[\large\rm qoutient + \frac{ remainder }{ divisor }\]
Oh. I'm not sure what the remainder/divisor would be. @Nnesha
|dw:1433977783733:dw| remainder that u get at the end after distributing 3 by divisor what did you get ?
|dw:1433977855878:dw| change sign at the end and then combine like terms what did yo uget
I think I got 3? @Nnesha
nope that's the quotient |dw:1433977995683:dw|
15x? Sorry, I don't really understand this part. @Nnesha
change sign |dw:1433978205001:dw| combine like terms