Question

Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)f(x) = 4x3 − 21x2 + 35x − 18; x − 1

Answer 1

We know that:

`f(x)=(x-1)p(x),`

where

`p(x)=(f(x))/(x-1).`

Using synthetic division, we get:

`(f(x))/(x-1)=4x^2-17x+18.`

Now, notice that:

`4x^2-17x+18=(x-2)(4x-9).`

Therefore:

`4x^3-21x^2+35x-18=(x-1)(x-2)(4x-9).`

Finally, we get that the zeros of the polynomial are:

`x=1,x=2,x=(9)/(4).`

Answer:

`x=1,x=2,x=(9)/(4).`