Answer:
x = a is a zero of a polinomial f(x), this is the same than: f(x) has a root at x = a
Then: f(a) = 0.
a) x = a is a ____ of the polynomial equation f(x) = 0.
If we define f(x) = 0, then x = a is a solution of the equation.
Then the complete sentence is:
x = a is a solution of the polynomial equation f(x) = 0.
b) ____ is a factor of the polynomial f(x).
Remember that if a polynomial p(x) of degree n has the roots x₁, x₂, ..., xₙ
Then we can write p(x) in the factorized form as:
p(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)
Where A is a real number.
Then if in this case we know that a is a root of f(x), then (x - a) is a factor of the polynomial f(x), then the complete sentence is:
(x - a) is a factor of the polynomial f(x).
c) (a, 0) is a ____ of the graph f(x)
We usually use the notation y = f(x).
Then the points of the form (x, f(x)) are the points that belong to the graph of f(x).
In this case, the point (a, f(a)) = (a, 0)
This point belongs to the graph of f(x), then the complete sentence can be written as:
(a, 0) is a point of the graph f(x).
