SOLUTION: f(x)=28x^4-8x^3-36x^2+112x-144 need to factor that completely. Then after that need to find all the zeros of the function.

Question 1085361: f(x)=28x^4-8x^3-36x^2+112x-144
need to factor that completely. Then after that need to find all the zeros of the function.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
28x^4-8x^3-36x^2+112x-144=
4(7x^4-2x^3-9x^2+28x-36)
synthetic division with -2
-2/7==-2==-9==28==-36
==7==-16--23---18===0
(x+2) is a factor (7x^3-16x^2+23x-18))
graphing this shows 9/7 as a root.
Therefore (7x-9) is a factor.
Multiply (x+2)(7x-9) to get 7x^2+5x-18
Divide that into the 7x^4-2x^3-9x^2+28x-36 and the result is x^2-x+2, which has complex roots.
roots are -2 and 9/7
factors are 4(x+2)(x^2-x+2)(7x-9)

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