Nala wants to determine if x-5 is a factor of p(x)=x^3-5x^2-x+5. nala organize her steps.
step 1-?
step 2-?
step 3-?
options:
1) apply the factor theorem, the remainder is 0 so x-5 is a factor of p(x)
2) apply the factor theorem, the remainder is not 0 so x-5 is not a factor of p(x)
3) evaluate p(x) for x=5
4) apply the polynomial theorem, the remainder is 0, so x-5 is a factor of p(x)
5) divide
6) simplify and find the remainder
7) evaluate p(x) for x=-5

I only used two steps: 3) then 6) then 1).

Step-by-step explanation:

Ok, if x-5 is a factor of p(x), then p(5)=0 by factor theorem.

This also goes the other way around:

If p(5)=0 then x-5 is a factor of p(x) by factor theorem.

Let's check. I'm going to evaluate p(x) for x=5.

This implies x-5 is a factor since we have p(5)=0.

The first step I did was 3) evaluate p(x) for x=5.

The second step I did 6) simplify and find the remainder. I did this when I was evaluating p(5); that was a lot of simplification and then I found the remainder to be 0 after that simplification. The last step was 1) apply the factor theorem, the remainder is 0 so x-5 is a factor of p(x).

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