Question

How do you use the factor theorem to determine whether 3x+1 is a factor of `f(x)= 3x^4 -11x^3 - 55x^2 + 163x + 60`?

Answer 1

`3x+1` is a factor of `f(x)`

Explanation:

Let's define `f(c)` to be equal to `3x+1`. Thus, the factor theorem tells us if `f(c)=0`, then `3x+1` is a factor of our polynomial `f(x)`.

Let's set `f(c)` equal to zero. We get

`3x+1=0`

`=>3x=-1`

`=>color(blue)(x=-1/3)`

Now, let's plug this value into our polynomial. This is a hairy problem, so let's not be ashamed to use a calculator. I did but had issues uploading the image, but this evaluates to zero.

Since it evaluated to zero, `3x+1` is a factor of `f(x)`.

Hope this helps!