Respuesta :
Answer: x - 2
Step-by-step explanation:
If p(2)+4=4, then p(2) = 0. Thus, the function has a zero at x = 2, and corresponding to that zero is the factor x - 2.
The binomial that is a factor of the polynomial P(x) is (x-4).
What is the remainder theorem of polynomials?
According to the remainder theorem of polynomials, if a polynomial function f(x) is divisible by a factor (x-a), and leaves no remainder then, the value of f(a) will be zero.
As it is given that the value of the polynomial function P(4)+2=2, therefore, the value can be written as,
[tex]P(4)+2=2\\\\P(4)=2-2\\\\P(4)=0[/tex]
As we can see that the value of the polynomial function at x=4 is 0, therefore, the binomial that is a factor of the polynomial P(x) is (x-4).
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