Determine which of the following polynomials has (x + 1) as a factor x^3-x^2-(3-√3)x+√3
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Step-by-step explanation:
Given polynomial is p(x)=x³-x²-(3-√3)x+√3
Given linear polynomial =(x+1)
We know that by factor theorem
Let p(x) be a polynomial of the degree is greater than or equal to 1 and another linear polynomial is (x-a) ,if p(a)=0 then (x-a) is a factor of p(x) and vice-versa.
given linear pilynomial is x+1=0=>x=-1
now,p(-1)=(-1)³-(-1)²-(3-√3)(-1)+√3
=>-1-1-+3-√3+√3
=>1≠0
So,(x+1) is not a factor of p(x).
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