Question

Use the factor theorem to determine whether g(x) is a factor of p(x) in the given expression p(x) = 2x³ + x^{​​​​​​2} - 2x - 1,g(x) = x + 1

Answer 1

Factor Theorem
Let f (x) be a polynomial. If a polynomial f (x) is divided by x = c, then the remainder will be zero. That is, x = c is zero or root of a polynomial f (x) , which also makes (x – c) is a factor of f (x). Thus, the theorem states that if f (c)=0, then (x–c) is a factor of the polynomial f (x). The converse of this theorem is also true. That is, if (x – c) is a factor of the polynomial f (x), then f(c)=0.
so the solution is here