need help factoring this polynomial: 2x^6 + 5x^4 - x^2

[m33r]

Please help factor the following polynomial and show the method you used:

2x^6+5x^4-x^2

Thanks.

 

[Deleted member 4993]

Please help factor the following polynomial and show the method you used:

2x^6+5x^4-x^2

Thanks.

Do you see any term common to all three?

If you do, first action would be to factor that out.

Now continue...

If you are still stuck write back showing your work.

 

[m33r]

Do you see any term common to all three?

If you do, first action would be to factor that out.

Now continue...

If you are still stuck write back showing your work.

Hey Khan, thanks for the reply.

There's

x^2( 2x^4 + 5x^2 - 1 )

That's as far as I was able to get.

 

[m33r]

Do you see any term common to all three?

If you do, first action would be to factor that out.

Now continue...

If you are still stuck write back showing your work.

Please find at this link:

https://www.dropbox.com/s/h1wygzmfdts5wqx/20170916_203148.jpg?dl=0

I basically tried synthetic division but wasn't able to solve.

 

[tkhunny]

Are you able to factor this? 2z^2 + 5z - 1

If not, can you apply the Quadratic Formula or Complete the Square on 2z^2 + 5z - 1 = 0 to gain some insight?

 

[mmm4444bot]

x^2( 2x^4 + 5x^2 - 1 )

That's as far as I was able to get.

Your later work using the Rational Root Theorem and synthetic division shows that the fourth-degree polynomial above has no Rational roots.

That's as far as you can go.

Another way to discover that it cannot be factored further (at least, not nicely) is to recognize, as tkhunny did, that the fourth-degree polynomial is quadratic in form; then use the Discriminant (b^2-4ac).

Let z = x^2

z(2z^2 + 5z - 1)

The Discriminant is 25-4(-2) = 33

In order for a quadratic polynomial to factor with Rational terms, the Discriminant must be the square of a Rational number. 33 is a prime number, not a square. Therefore, the quadratic does not factor nicely. :cool: