Solving 6x^3 - 3x^2 - 45x Equation

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Homework Help Overview

The discussion revolves around the polynomial equation 6x^3 - 3x^2 - 45x, with participants attempting to factor and solve it. The subject area includes polynomial equations and factoring techniques.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss factoring out common terms and simplifying expressions. There are questions about the correctness of steps taken, particularly regarding the factorization process and the need for an equation format. Some participants suggest using the quadratic formula for further analysis.

Discussion Status

The discussion is active, with participants providing feedback on each other's attempts and clarifying misunderstandings. Some guidance has been offered regarding the factorization process, and there is recognition of mistakes made in earlier steps. Multiple interpretations of the problem are being explored.

Contextual Notes

There is a noted confusion regarding the original equation's format, as some participants question whether it should include an equals sign. Additionally, there are discrepancies in the arithmetic calculations presented in the attempts.

Corkery
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Homework Statement


6x^3 - 3x^2 - 45x


Homework Equations





The Attempt at a Solution


-first factor out 3x
3x(2x^2 - x -15)

2 x 5 = 30 so...

3x(2x^2 + 5x - 6x - 15)

-separate the equations
3x(2x^2 + 5x)( - 6x -15)

-simplify a few things.
3x^2(2x + 5) -3 (2x + 5)

(3x^2 - 3)(2x + 5)

set both equations to zero
2x + 5 = 0
2x = -5
x = -5/2

3x^2 - 3 = 0
3x^2 = 3

thats where I get stuck, that is if I did this right. thanks for any help you can offer.
 
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Corkery said:

Homework Statement


6x^3 - 3x^2 - 45x


Homework Equations





The Attempt at a Solution


-first factor out 3x
3x(2x^2 - x -15)

2 x 5 = 30 so...

3x(2x^2 + 5x - 6x - 15)
What've you done to get from the line above to this:
-separate the equations
3x(2x^2 + 5x)( - 6x -15)
It's incorrect, anyway. You should try using the quadratic formula to factorise (2x^2 -x- 15)
 
Corkery said:

Homework Statement


6x^3 - 3x^2 - 45x
Wasn't this supposed to be an equation? And, if so, doesn't it need an "=" somewhere? Did you mean 6x^3- 3x^2- 45x= 0?

Homework Equations





The Attempt at a Solution


-first factor out 3x
3x(2x^2 - x -15)

2 x 5 = 30 so...
Well, no, 2 x 5= 10, not 30. But there is no 30 in the equation anyway so I don't know what you were trying to do!

3x(2x^2 + 5x - 6x - 15)

-separate the equations
3x(2x^2 + 5x)( - 6x -15)
?? Did you mean 3x[(2x^2+ 5x)+ (-6x-15)]?

-simplify a few things.
3x^2(2x + 5) -3 (2x + 5)
Again, you mean 3x^2[(2x+5)- 3(2x+5)]

(3x^2 - 3)(2x + 5)
No, since the 3x is multiplied by both 2x+ 5 and -3(2x+5) you cannot separate the expression like that.
set both equations to zero
2x + 5 = 0
2x = -5
x = -5/2

3x^2 - 3 = 0
3x^2 = 3

thats where I get stuck, that is if I did this right. thanks for any help you can offer.
Well, obviously that gives x^2= 1 which has solutions x= 1 and x= -1- but they obviously do not satisfy the original equation. Go back to 3x^2(2x^2 - x -15)= 0. That gives you one obvious solution. Now try to factor 2x^2- x- 15.

However, this equation does not has complex roots!
 
Last edited by a moderator:
ok thanks a lot. that really does help a lot. My tutor also pointed out some of my mistakes, but with the combination of that and this I'm very clear on the subject. thanks again
 

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