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

- anonymous

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

- Stacey Warren - Expert brainly.com

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- chestercat

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- Nnesha

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

- Loser66

I believe the problem is "simplify" instead of "solve"

- Nnesha

divide first terms \[\rm \frac{ -18x^3 }{ 3x } = ??\]

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## More answers

- anonymous

=-6x^3? @Nnesha

- Nnesha

x^3 can be written as x times x times x
so \[\rm \frac{ x \times x \times x }{ x } = ??\]

- anonymous

x^3?
@Nnesha

- Nnesha

nope
you can cancel one x right ?

- Nnesha

\[\rm \frac{ x \times x \times \cancel x }{ \cancel x } = ??\]

- anonymous

Ok! So x^2?
@Nnesha

- Nnesha

yes right!

- Nnesha

now 2nd step |dw:1433975352357:dw|
distribute divisor by
-6x^2
so -6x^2 (3x+2)

- anonymous

So -18x^2 +4?
@Nnesha

- Nnesha

nope
when you multiply same bases you should add their exponents

- anonymous

I understand. So 18x^3+4
@Nnesha

- 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 =?

- Nnesha

yes x^3 is right but there is a little mistake :-)

- anonymous

So 18x^3 and 12x^2?
@Nnesha

- Nnesha

you forgot negative sign

- anonymous

Oh yeah! So -18x^3 and -12x^2?
@Nnesha

- Nnesha

there you go!

- Nnesha

|dw:1433975913009:dw|
step 3 change sign and then combine like terms :-)

- anonymous

So 12x^2+17x+6?
@Nnesha

- Nnesha

yes right! now repeat!

- Nnesha

|dw:1433976142678:dw|
divide first terms
12x^2/3x

- anonymous

Ok so 4x?
@Nnesha

- Nnesha

yep!

- anonymous

And the next step is to divide 6 by 2? So would the answer be -6x^2+4x+3?
@Nnesha

- Nnesha

6 by 2 ??

- Nnesha

4x right
now 2nd step distribute!

- anonymous

Sorry, I'm confused with what to do next.
@Nnesha

- Nnesha

1st step is divide you did that now 2nd step distribute 4x by divisor

- anonymous

ok so do I divide 17x by 4x now?
@Nnesha

- Nnesha

alright nope you don't have to divide by quotient |dw:1433976642990:dw|
divide first terms
remember 3x stay same

- Nnesha

you got 4x now distribute divisor by 4x
4x(3x+2) = ?

- Nnesha

|dw:1433976698488:dw|

- anonymous

So 12x+8x?
@Nnesha

- Nnesha

remember when you multiply same bases you should add their exponents
so 4x times 3x = ?

- anonymous

12x^2
@Nnesha

- Nnesha

yep right :-)

- Nnesha

|dw:1433976885337:dw|
try!

- anonymous

Ok so -6x^2+4x+3?
@Nnesha

- Nnesha

is that the quotient ?

- anonymous

I think so
@Nnesha

- anonymous

Is that the correct answer? @Nnesha

- Nnesha

is that a guess ?

- anonymous

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

- Nnesha

alright |dw:1433977488813:dw|
yes that's right
9x/3x = 3

- anonymous

Ok is that all I had to do for that question?
@Nnesha

- Nnesha

that's just quotient what is the remainder
answer should be like this \[\large\rm qoutient + \frac{ remainder }{ divisor }\]

- anonymous

Oh. I'm not sure what the remainder/divisor would be.
@Nnesha

- Nnesha

|dw:1433977783733:dw|
remainder that u get at the end
after distributing 3 by divisor
what did you get ?

- Nnesha

|dw:1433977855878:dw|
change sign at the end and then combine like terms what did yo uget

- anonymous

I think I got 3? @Nnesha

- Nnesha

nope that's the quotient |dw:1433977995683:dw|