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Question 159653: Pls , help me to solve this problem"
(2x^3+x^2)-(8x-4)=0
Thanks
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! (2x^3+x^2)-(8x-4)= 0
The first thing you want to do is remove the parentheses.
Do you see the negative sign in front of the quantity -(8x-4)?
Believe it or not, there is an invisible -1 there. You must multiply -1 by every term inside the parentheses.
So, let's do that first.
-1 times 8x = -8x
-1 times -4 = 4
We no have this equation:
2x^3+x^2 -8x + 4 = 0
We make two groups here:
2x^3+x^2...GROUP A
-8x + 4...Group B
We factor each group separately.
2x^3+x^2 becomes x^2(2x + 1)
-8x + 4 becomes -4(2x - 1)
We now have three factors:
(x^2 - 4), (2x + 1) and (2x - 1)
We equate each factor to zero and solve for x.
x^2 - 4 = 0
x^2 = 4
We take square root of both sides and get x = -2 and x = 2
=============================
2x + 1 = 0
2x = -1
x = -1/2
=============================
2x - 1 = 0
2x = 1
x = 1/2
==============================
We have 4 values of x:
x = -2, x = 2, x = -1/2 and x = 1/2
Are they all values of x?
The only way to find is to plug all found values of x into the original equation...the equation that was given to you and simplify.
If you get the same answer on both sides of the equation, then you will know which is the correct value of x or if they all are correct values of x.
I'll let you do the checking.
If you do not understand what I did , write back.
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You said:
"Thanks for your promptly reply....Still have a quesion...Why you need to separate the original equation in 2 parts?? Why you need to factorize each one and the final one...How can I identify when is needed to separate & calculate the factor in an equation?"
My New Reply:
I separated the original equation into two parts to do something that is called factoring by groups. When you have a polynomial of 4 terms, the easiest way to factor is to set up two groups, factor each group individually, set each factor to zero and solve for x.
To check your values of x, plug every value of x that you found into the original polynomial given.
If you get the same answer on both sides of the equation, you will know that your values of x are right.
Do you understand?
If not, write back.
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