Posted by **Sara** on Sunday, January 15, 2012 at 1:30pm.

I'm going to do this on my own, but I would like to check mine against yours - give me today to work on it and I will be able to compare. List all possible rational zeros for the polynomial find all real zeros and factor completely. show work

f(x)=3x^4-29x^3+89x^2-75x-36

thank you.

- precalculus -
**Reiny**, Sunday, January 15, 2012 at 5:15pm
good for you

Tried x + ±1, ± 2, ±3

found f(3) = 0

so by synthetic division

(x-3)(3x^3 - 20x^2 + 29x + 12)

found x = 4 works in 2nd bracket, so x-4 is a factor

another synthetic division .....

so far

(x-3)(x-4)(3x^2 - 8x - 3)

and the quadratic factored again

= (x-3)9x-4(x-3)(3x + 1)

= (x-4)(3x+1)(x-3)^2 , double root at x=3

so x = - 1/3, 3, 4

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