Math genius needed please. Factoring polynomials and Simplifying Rational expressions.?

Question

I tried to do this question but I am having difficulties:(
3x^3+27x
Can you please explain the steps to me and show me the work please and thank you very very much:)
Have a wonderful weekend!

please can someone explain the steps to me?

Answer 1

You dont need a Math genius for that, just to use the distributive property

3x(x^2 + 9)

Ilusion

EDIT

This about this:

3(x+1) = 3x + 3

Now: What if you have 3x + 3 and you want to find out how to factorize it? You observe that you have a 3 in every term, so, you know that you can have this 3 "out" and mutiplied by something, this way:

3 (...+....) or 3 (... - .. )

What about the sign? It must be a +. Why? Because, if it was a -, the result of the distributive (3 multiplied by something negative) would never have been a +

So, now we have to find out how to fill in these blanks.

3 (.... + .... ) = 3x + 3

Which number, multiplied by 3, gives you 3? Only 1

Which leter, multiplied by 3, gives you 3x? x

So, the answer is: 3(x+3)

Now lets come back to your problem

3x^2 + 27 x

You can factor a 3. Remember that 3*9 = 27

So, you have 3(x^3+ 9 x). If you have doubts, multiply these expression and check that you get 3x^3 + 27 x

Now, we can factorize this again. Both term have at least an x as a factor. We can do the same than we did with the 3

3x (x^2 + 9)

Remember that x^3 = x*x*x

If you write one x "out", the other 2 will be "in".

Hope this helps you understand.

Write to me if this is still unclear to you

Ilusion

Answer 2

Look at what factors these two terms have in common:
3x^3 + 27x

Both terms have at least one "x", so you can factor that out as being common to both. So basically we're using the distributive property in reverse:
x(3x^2 + 27)

Now 27 is a multiple of 3, so we can factor out a 3 from both:
3x(x^2 + 9)

It's possible to factor out x^2 + 9 using complex numbers, but I suspect you haven't covered that yet. So we'll just leave this as is.

Answer 3

3x^3+27x=

Take 3x out of the equation
3x which leaves you with x^2+9

3x(x^2+9)

Answer 4

That's the sum of 2 cubes. The easiest way to remember this is that a+b is always a factor. If you forget the second factor, you can always recover it by long division. The factors are (a+b)(a²-ab+b²).

Answer 5

3x^3+27x=3x(x^2+9)

Answer 6

Factor out 3x to begin with:
3x(x^2 + 9) = 3x(x+9i)(x-9i)

Answer 7

3x^3+27x =
3x(x^2 + 9)
3x(x + j3)(x - j3)
j = √-1