nala wants to determine if x-5 is a factor of p(x)=x^3-5x^2-x+5. Help 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=54) apply the polynomial theorem, the remainder is 0, so x-5 is a factor of p(x)5) divide6) simplify and find the remainder 7) evaluate p(x) for x=-5

Answer: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.[tex]p(5)=5^3-5(5)^2-5+5[/tex][tex]p(5)=125-5(25)-5+5[/tex][tex]p(5)=125-125-5+5[/tex][tex]p(5)=0+0[/tex][tex]p(5)=0[/tex]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).