Respuesta :
Answer:
One factor is x+1.
Step-by-step explanation:
f(x) = x^3 - x^2 - 3x - 1.
The factor theorem states that if x-a is a factor of f(x) then f(a) = 0.
Try x = 1 (to see if (x-1) is a factor:
f(1) = 1 - 1 - 3 - 1 = -4. This is not zero so x-1 NOT a factor.
Try f(-1) = -1 - 1 + 3 - 1 = -3 + 3 = 0
So x+1 is a factor.
The one factor of the given polynomial is (x + 1).
What is polynomial?
A polynomial is an expression that consists of variables (or indeterminate), terms, exponents and constants.
What is factor theorem?
According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number then, (x-a) is a factor of f(x), if f(a)=0.
According to the given question
We have a polynomial
[tex]f(x) = x^{3} -x^{2} -3x-1[/tex]
For finding the factors of the given polynomial, substitute f(x) = 0.
⇒[tex]x^{3} -x^{2}-3x-1=0[/tex]
⇒ [tex](x+1)(x^{2} -2x-1)=0[/tex]
Therefore, the one factor of the given polynomial is (x + 1).
Learn more about factor theorem here:
https://brainly.com/question/17092136
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