"Use the Factor Theorem (x-b is a factor of P(x) if and only if P(b)=0) to factor the polynomial completely or to prove that it has no linear factors with integer coefficients"

x^3+9x^2+24x+20

Could you please walk me through how to do this? Thank you! :)

Question

"Use the Factor Theorem (x-b is a factor of P(x) if and only if P(b)=0) to factor the polynomial completely or to prove that it has no linear factors with integer coefficients"

x^3+9x^2+24x+20

Could you please walk me through how to do this? Thank you! :)

ranga · Answer

Try a few small values for x and see when it becomes 0.
x^3+9x^2+24x+20
This function has all positive coefficients and therefore it will not go to 0 for any positive values of x.
So try x = -1, -2, -3, etc.  
As soon as you find one root, do synthetic division and find the quotient which will be a quadratic and you can find the roots using the quadratic formula.

ajoy31 · Answer

okay, so I got that if x=-2, the equation would be 0. how do I plug this in to synthetic division?

ranga · Answer

-2 |    1      9      24      20
     |  
     |___________________________

ajoy31 · Answer

Okay. Cool. Thank you! :)

ranga · Answer

you are welcome.