Question

One of the zeros of the polynomial function is 2. f(x)=x4−3x3−23x2+75x−50 What is the factored form of the function?

Answer 1

In order to find the factored form  of the function you have to follow those steps

we have

$f\left(x\right)=x^4-3x^{3\ }-23x^2+75x-50$

we know that

The zeros of the function are the values of x when the function is equal to zero

so

Step 1

Using a graphing tool -------> find the zeros of the polynomial

see the attached figure

The zeros are

$x=-5\ x=1\ x=2\ x=5$

Step 2

Find the factored form

$f\left(x\right)=x^4-3x^{3\ }-23x^2+75x-50=(x+5)(x-1)(x-2)(x-5)$

therefore

the answer is

$f\left(x\right)=(x+5)(x-1)(x-2)(x-5)$

Answer 2

f(x)=(x−5)(x+5)(x−2)(x−1)