I do not know how to solve this question. 5x

^{3}+30x=0I do not know how to solve this question. 5x^{3}+30x=0

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Middletown, CT

Hi LaTanya;

5x^{3}+30x=0

For the FOIL, we know that...

FIRST must be (5x^{2})(x) or (x^{2})(5x)

LAST must include 0, (?)(0) or (0)(??)

There are four ways to factor this.

(5x^{2}+30)(x+0)=0

FOIL...

FIRST...(5x^{2})(x)=5x^{3}

OUTER...(5x^{2})(0)=0

INNER...(30)(x)=30x

LAST...(30)(0)=0

Factored...

(5x^{2}+30)(x+0)=0

Either parenthetical equation can be equal to zero...

5x^{2}+30=0 or (x+0)=0

5x^{2}=-30 or x=0

x^{2}=-30/5

x^{2}=-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...

(x^{2}+6)(5x+0)=0

FOIL...

FIRST...(x^{2})(5x)=5x^{3}

OUTER...(x^{2})(0)=0

INNER...(6)(5x)=30x

LAST...(6)(0)=0

(x^{2}+6)(5x+0)=0

Either parenthetical equation can be =0.

x^{2}+6=0 or 5x+0=0

x^{2}=-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...

(-x^{2}-6)(-5x+0)=0

FIRST...(-x^{2})(-5x)=5x^{3}^{
}

OUTER...(-x^{2})(0)=0

INNER...(-6)(-5x)=30x

LAST...(-6)(0)=0

(-x^{2}-6)(-5x+0)=0

-x^{2}-6=0 or -5x+0=0

-x^{2}=6 or x=0

x=0 is the only solution.

******************

Let's factor again...

5x^{3}+30x=0

5x(x^{2}+6)=0

x=0, to produce 5x as 0, is one solution.

x^{2}+6=0

x^{2}=-6 cannot be resolved to a positive number.

The only solution is x=0

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