What is the simpler form of the following expression?
(-18x^3+17x+6)÷(3x+2)
A. -6x^2+4x+3
B. 6x^2+4x-3
C. -6x^2+4x-3
D. 6x^2-4x+3
C. -6x^2+4x-3
AAAaannndd the bot gets it wrong yet again!
(-18x^3+17x+6) = (3x+2)(-6x^2+4x+3)
So, A
is the correct answer. Thank you for letting me know of my mistake.
To find the simpler form of the given expression, we need to perform the division of the polynomial (-18x^3 + 17x + 6) by (3x + 2).
Let's use long division to simplify the expression:
```
-6x^2 + 4x - 3 Remainder
___________________________________
3x + 2 | -18x^3 + 0x^2 + 17x + 6
- (-18x^3 - 12x^2)
_______________________
12x^2 + 17x
- (12x^2 + 8x)
_______________
9x + 6
- (9x + 6)
___________
0
```
From the long division, we can see that the remainder is 0, indicating that the polynomial (-18x^3 + 17x + 6) is completely divisible by (3x + 2). The quotient is -6x^2 + 4x - 3. Therefore, the simpler form of the expression is -6x^2 + 4x - 3.
The correct answer is C. -6x^2 + 4x - 3.