Is (x + 7) a factor of f(x) = x^3 − 3x^2 + 2^x − 8? Use either the remainder theorem or the factor theorem to explain your reasoning.

Answer:Not a factorStep-by-step explanation:We can use Factor Theorem to answer this question. According to this theorem, in order to find if (x - a) is a factor of a polynomial f(x), calculate f(a). If f(a) comes out to be equal to zero, this will mean that (x-a) is  factor of f(x).Here, the expression we have is (x + 7), so we need to find f(-7) in order to check if (x+7) is a factor of f(x) or not[tex]f(x)=x^{3}-3x^{2}+2x-8[/tex]Substituting x = -7, we get:[tex]f(-7)=(-7)^{3}-3(-7)^{2}+2(-7)-8\\\\ f(-7)=-512[/tex]Since f(-7) ≠ 0, (x + 7) is not a factor of the polynomial f(x)