Question

solve( -18x^3+17x+6)/(3x+2)

Answer 1

HELP

Answer 2

Is this multiple choice?

Answer 3

try change (-18x^3+17x+6) into (3x+2)(ax+b) form

Answer 4

How can you solve this? There is no equation.

Answer 5

I believe she wants the quotient and remainder.

Answer 6

@wolfe8 in this case solve would mean simplify

Answer 7

Simplify the following:
(-18 x^3+17 x+6)/(3 x+2)
Factor a minus sign out of -18 x^3+17 x+6.
Factor -1 out of -18 x^3+17 x+6:
-(18 x^3-17 x-6)/(3 x+2)
Find all linear factors of 18 x^3-17 x-6 via the rational root theorem. Do this by finding rational roots. The candidates are x = ±p/q for all p that are divisors of the constant term -6 and for all q that are divisors of the leading coefficient 18.
The possible rational roots of 18 x^3-17 x-6 are x = ±1/18, x = ±1/9, x = ±2/9, x = ±1/6, x = ±1/3, x = ±2/3, x = ±1/2, x = ±3/2, x = ±1, x = ±2, x = ±3, x = ±6. Of these, x = -2/3 is a root. This gives 3 x+2 as all linear factors:
-(((3 x+2) (18 x^3-17 x-6))/(3 x+2))/(3 x+2)
Divide 3 x+2 into 18 x^3-17 x-6.
| |
3 x | + | 2 | | 6 x^2 | - | 4 x | - | 3
18 x^3 | + | 0 x^2 | - | 17 x | - | 6
18 x^3 | + | 12 x^2 | | | |
| | -12 x^2 | - | 17 x | |
| | -12 x^2 | - | 8 x | |
| | | | -9 x | - | 6
| | | | -9 x | - | 6
| | | | | | 0:
-(6 x^2-4 x-3 (3 x+2))/(3 x+2)
Cancel common terms in the numerator and denominator of -((3 x+2) (6 x^2-4 x-3))/(3 x+2).
-((3 x+2) (6 x^2-4 x-3))/(3 x+2) = (3 x+2)/(3 x+2)×-(6 x^2-4 x-3) = -(6 x^2-4 x-3):
Answer: |
| -(6 x^2-4 x-3)

Answer 8

Much neater:

Answer 9

\[9x + 6 - 9x + 6 = 0\]
So the remainder is zero, the and the quotient is: \[-6x^2 + 4x +3\]