factoring?

Question

i need help. i don't understand this--

solve the equation:

3x³- 27x = 0

by factoring.


-thanks =)

Answer 1

factor out a 3x

3x((x^2)-9)=0

3x=0 (x^2)-9=0
x=0, x=3, -3

Answer 2

Factoring is when you remove a common element, or "factor", from all parts of an equation. In this case(note: the ^ symbol denotes that the number is raised to a power by the number after the ^, so x^2 is x squared):

3x^3-27x=0

If you remove 3x from each of the components on the left side, you're left with this equation:

3x(x^2-9)=0

The equation is still the same as above, the parentheses indicates that 3x should be multiplied by both the numbers inside, which would take you back to your original equation.

To solve the problem, you just solve each of the parts seperately, so you have:

3x=0 and (x^2-9)=0

The answer to the first part can only be x=0. The second part changes into x^2=9 by adding 9 to both sides. The answer to this part is either -3 or 3.

So, your answer to the entire problem is that x=-3,0, or 3.

Answer 3

It means find the values of x that will cause the equation to equal zero.

Factor out a 3x to get:

3x(x^2 - 9) = 0

Then you can easily see that when x=0, 3, and -3, the equation will equal 0. There you go.

You always want to factor out the greatest coefficient and variable power that you can. In this case, the greatest coefficient that could be factored was 3, and the greatest variable power was x^1 or just x.

If the problem was:
9x^9 + 63x^6 - 27x^3 = 0
You would then want to factor out 9x^3:
9x^3(x^3 + 7x^2 - 3) = 0
Thus making the problem much easier to solve than initially.

Answer 4

since it's 3x^3 so:
factor out 3x

3x(x^2 - 9)=0

3x=0
x = 0

and

x^2 = 9
x = square root of 9
x = +3, -3

Answer 5

3x(x^2-9)=0
3x(x-3)(x+3)=0
x=0,3,-3