Factorizing a Cubic Equation: How Do I Solve (x-1)(2x-1)(3x-1) = 0?

In summary, to solve the equation (x-1)(2x-1)(3x-1) = 0, you can use the zero product property and set each factor equal to 0 to find the possible values of x. In this case, the solutions are x=1, x=1/2, and x=1/3.
  • #1
Mo
81
0
I know how to solve quadratics using both factorisation and the equation method ... but how can i solve :

[tex](x-1)(2x-1)(3x-1) = 0 [/tex]

I multiplied it all out and i got ..

[tex]6x^3 - 2x^2 -3x -1=0[/tex]

I just do not know where to got from here .. a little nudge in the right direction would be appreciated!

regards,
Mo
 
Physics news on Phys.org
  • #2
Mo said:
I know how to solve quadratics using both factorisation and the equation method ... but how can i solve :

[tex](x-1)(2x-1)(3x-1) = 0 [/tex]

I multiplied it all out and i got ..

[tex]6x^3 - 2x^2 -3x -1=0[/tex]

I just do not know where to got from here .. a little nudge in the right direction would be appreciated!

regards,
Mo

A small hint: why do you multiply? After all, if a*b*c=0, then...
 
  • #3
Mo said:
I know how to solve quadratics using both factorisation and the equation method ... but how can i solve :
[tex](x-1)(2x-1)(3x-1) = 0 [/tex]
I multiplied it all out and i got ..
[tex]6x^3 - 2x^2 -3x -1=0[/tex]
I just do not know where to got from here .. a little nudge in the right direction would be appreciated!
regards,
Mo

Why the heck did u multiply it? It was already solved.U were being asked for the 3 possible values of "x" which cancel the expression from the LHS.I think/hope they were obvious...

Daniel.

PS.But if u'd rather apply Cardano's formulae for the 3rd order algebrac equation u got,be my guest... :-p
 
  • #4
:blushing:

yes, i do understand.

if

(x-1) = 0 then x =1
(2x-1) =0 then 2x=1 so x = 1/2
(3x-1) = 0 then 3x=1 so x=1/3

is that right.Am i going about it right. thanks.
 
  • #5
Yeah, that's right.
 

FAQ: Factorizing a Cubic Equation: How Do I Solve (x-1)(2x-1)(3x-1) = 0?

How do I factorize a polynomial?

To factorize a polynomial, you need to find its factors, which are expressions that can be multiplied together to get the original polynomial. You can use various methods such as grouping, difference of squares, or trial and error to factorize a polynomial.

What is the difference between factorizing and simplifying a polynomial?

Factorizing and simplifying a polynomial are two different processes. Factorizing involves finding the factors of a polynomial, while simplifying involves reducing a polynomial to its simplest form by combining like terms and removing any unnecessary parentheses.

Can all polynomials be factorized?

No, not all polynomials can be factorized. Some polynomials may not have any factors, while others may have factors that cannot be easily determined. In these cases, the polynomial is said to be "prime" and cannot be factorized any further.

How do I know if I have factored a polynomial correctly?

You can check if you have factored a polynomial correctly by multiplying out the factors. If the result is the original polynomial, then you have factored it correctly. You can also use the distributive property to check if the factors are correct.

Can I use a calculator to factorize a polynomial?

Yes, there are many calculators and online tools available that can help you factorize a polynomial. However, it is important to understand the concept and steps involved in factorizing a polynomial rather than relying solely on a calculator.

Similar threads

Solving for x in 0 = -1/8 + 3/8 x / (10^2 +x^2)^0.5
Replies
10
Views
2K
##\int_0^1 F_x(x,0)dx + \int_0^1 F_y(1,y)dy##
Replies
7
Views
1K
MHB Equation 2: Prove that ##x^2+2x\sqrt x+3x+2\sqrt x+1=0##
Replies
4
Views
1K
I Different Substitution for Solving an Integral
Replies
6
Views
719
Solve ##x^{\frac{-1}{2}}-2x^{\frac{1}{2}}+x^{\frac{2}{3}}=0##
Replies
24
Views
1K
Particle constrained on a curve
Replies
9
Views
2K
Understanding Cubic Factorization: Solving for Roots with a and -2a
Replies
6
Views
921
Show that if ##x>1##, ##\log_e\sqrt{x^2-1}=\log_ex-\dfrac{1}{2x^2}-##
Replies
8
Views
2K
Direction of friction for three bodies stacked one on top of the other
Replies
13
Views
2K
Multipole Expansion: Show that the quadrupole moment is symmetric and that the trace vanished
Replies
10
Views
529

Hot Threads

Recent Insights

Back
Top