5x^3+30x=0

Question

I do not know how to solve this question.  5x³+30x=0

Answer 1

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