Question

Given the polynomial function

f (x) = x^3 – 4x^2 + x + 6
1) Name all of the possible roots for the function using the Rational Root Theorem.

2) Prove 2 is one of the zeroes of this function (show or describe your process).

3) Name the three actual roots of this function and describe how you found them.

4) Write the original polynomial function in factored form and describe how you
found those factors.

Answer 1

3) x = -1, 2, 3

Explanation:

2)

x is a root of this function, so when we put x=2 in this function, we'll get f(x)=( 2+1 )*( 2-2 )*( 2-3 ). Because 2-2=0, so the function will equals to zero, too.

3)

By factorizing f (x) = x^3 – 4x^2 + x + 6, we can get ( x+1 )*( x-2 )*( x-3 )=0,

and if one of those three parts is zero, that the whole formula will be zero, now we get : x+1=0 or x-2=0 or x-3=0, so x can be -1, 2, or 3.

//sorry that I only could solve question 2 and 3...