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5x^3+30x=0

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1 Answer

Hi LaTanya;
5x3+30x=0
For the FOIL, we know that...
FIRST must be (5x2)(x) or (x2)(5x)
LAST must include 0, (?)(0) or (0)(??)
 
There are four ways to factor this.
 
(5x2+30)(x+0)=0
FOIL...
FIRST...(5x2)(x)=5x3
OUTER...(5x2)(0)=0
INNER...(30)(x)=30x
LAST...(30)(0)=0
 
Factored...
(5x2+30)(x+0)=0
Either parenthetical equation can be equal to zero...
5x2+30=0 or (x+0)=0
5x2=-30    or x=0
x2=-30/5
x2=-6
The first parenthetical equation does NOT work.  There is no such thing as the square root of a negative number.
However, one possibility is...
x=0
****************
Let's factor again...
(x2+6)(5x+0)=0
FOIL...
FIRST...(x2)(5x)=5x3
OUTER...(x2)(0)=0
INNER...(6)(5x)=30x
LAST...(6)(0)=0
 
(x2+6)(5x+0)=0
Either parenthetical equation can be =0.
x2+6=0  or  5x+0=0
x2=-6     or  5x=0, x=0
This also produced the only result of x=0 because there is no such thing as a the square root of a negative number.
x=0
***************
Let's factor again...
(-x2-6)(-5x+0)=0
FIRST...(-x2)(-5x)=5x3
OUTER...(-x2)(0)=0
INNER...(-6)(-5x)=30x
LAST...(-6)(0)=0
(-x2-6)(-5x+0)=0
-x2-6=0 or -5x+0=0
-x2=6    or x=0
x=0 is the only solution.
******************
 
Let's factor again...
5x3+30x=0
5x(x2+6)=0
x=0, to produce 5x as 0, is one solution.
x2+6=0
x2=-6 cannot be resolved to a positive number.
 
The only solution is x=0
 
 

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