What've you done to get from the line above to this: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)
It's incorrect, anyway. You should try using the quadratic formula to factorise (2x^2 -x- 15)-separate the equations
3x(2x^2 + 5x)( - 6x -15)
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?Corkery said:Homework Statement
6x^3 - 3x^2 - 45x
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!Homework Equations
The Attempt at a Solution
-first factor out 3x
3x(2x^2 - x -15)
2 x 5 = 30 so...
?? Did you mean 3x[(2x^2+ 5x)+ (-6x-15)]?3x(2x^2 + 5x - 6x - 15)
-separate the equations
3x(2x^2 + 5x)( - 6x -15)
Again, you mean 3x^2[(2x+5)- 3(2x+5)]-simplify a few things.
3x^2(2x + 5) -3 (2x + 5)
No, since the 3x is multiplied by both 2x+ 5 and -3(2x+5) you cannot separate the expression like that.(3x^2 - 3)(2x + 5)
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.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.
To solve this equation, you can use the factoring method. First, factor out the common factor of 3x. This leaves you with 3x(2x^2 - x - 15). Next, factor the quadratic expression inside the parentheses. This gives you 3x(2x + 5)(x - 3). So the solutions to the equation are x = 0, x = -5/2, and x = 3.
No, the quadratic formula can only be used to solve equations in the form ax^2 + bx + c = 0. Since this equation is a cubic, you will need to use a different method, such as factoring or the cubic formula.
This equation has three solutions, since it is a cubic equation. This is because any cubic equation can have up to three real solutions.
Solving this equation can help you find the values of x that make the equation true. This can be useful in various applications, such as finding the roots of a polynomial function or determining the points of intersection between two graphs.
Yes, you can use a calculator to solve this equation. However, it is important to understand the steps involved in solving the equation without a calculator, as it can help you better understand the concept of solving equations and check your answers for accuracy.