Factoring Problem

[rafirank]

Could someone please show me how to factor x to 5 power, 2x to third power, minus x squared, minus 2

 

[mmm4444bot]

Is this homework? What methods have you seen?

For example, have you learned about roots of polynomials?

Or, have you used the Remainder Theorem or the Factor Theorem?

Can you do polynomial long division or synthetic division?

Did you try any stuff? Where are you stuck?

If you need links to lessons on the topics above, please let us know.

Cheers :cool:

PS: This is how we text polynomials,

x^5 + 2x^3 - x^2 - 2

 

[rafirank]

I don't know how to get the arrow pointing up and yes I do know how to factor polynomials but I am just stuck on this one.

 

[rafirank]

Got it! thank you so much!

 

[mmm4444bot]

I do know how to factor polynomials

but I am just stuck on this one.

Okay, so you have factored higher-order polynomials before, but you got stuck somewhere on this exercise.

Please show us what you tried.

Here is a link to a summary of the posting guidelines.

 

[Deleted member 4993]

Remember:

a³ - b³ = (a - b)(a² + ab + b²)

 

[soroban]

Hello, rafirank!

\(\displaystyle \text{Factor: }\: x^5 + 2x^3 - x^2 - 2\)

\(\displaystyle x^5 + 2x^3 - x^2 - 2 \;=\;x^3(x^2+2) - 1(x^2+2)\)

. . . . . . . . . . . . . . \(\displaystyle =\; (x^2+2)(x^3-1)\)

. . . . . . . . . . . . . . \(\displaystyle =\; (x^2+2)(x-1)(x^2+x+1)\)

 

[rafirank]

Thank you everyone. I got the answer.
Rafi

 

[lookagain]

x^5 + 2x^3 - x^2 - 2

Why not this simple:
x^3(x^2 + 2) - (x^2 + 2)
(x^2 + 2)(x^3 - 1)

What you wrote isn't fully factored over rational coefficients.