Factoring Polynomial w/ Prime Coefficient

I am trying to factor $\displaystyle 3x^4 + 4x^3 -19x^2 -8x +12$ into 4 factors to continue solving. I tried by grouping, but it didn't get me anywhere since 19 is prime (all zeros are rational). I also tried factoring out GCFs (x^{2 }and x), but to no avail.

Re: Factoring Polynomial w/ Prime Coefficient

Hey ReneG.

Hint: There is a way to factor a quartic exactly using a formula figured out a while ago.

https://en.wikipedia.org/wiki/Quarti...mula_for_roots

Re: Factoring Polynomial w/ Prime Coefficient

Try substituting various values of x, looking for a value that makes the polynomial zero.

If x=a (say) makes the polynomial zero then (x-a) will be a factor.

Factor this out and repeat the process on the lower degree polynomial.

Start with x=1,2,-1,-2,... .

Re: Factoring Polynomial w/ Prime Coefficient

Quote:

Originally Posted by

**ReneG** I am trying to factor $\displaystyle 3x^4 + 4x^3 -19x^2 -8x +12$ into 4 factors to continue solving. I tried by grouping, but it didn't get me anywhere since 19 is prime (all zeros are rational). I also tried factoring out GCFs (x^{2 }and x), but to no avail.

Have a look at this.