Answer:
x + 3 is a factor of the polynomial.
Step-by-step explanation:
We have been given that p(x) is a polynomial with integer coefficient.
Also p(-3)=0
Since, p(-3) =0, hence, we can say that -3 is a zero of the polynomial.
Now, we apply factor theorem.
Factor Theorem: If 'a' is a zero of a function f(x) then (x-a) must be a factor of the function f(x).
Applying this theorem, we can say that (x+3) must be a factor of the polynomial.
Hence, first statement must be true.
Answer: The correct option is (A) (x + 3) is a factor of the polynomial.
Step-by-step explanation: Given that p(x) is a polynomial with integer coefficients and p(-3)=0.
We are to select the true statement from the given options.
Factor Theorem: If q(x) is a polynomial with integer coefficients and q(a) = 0, then (q - a) will be a factor of q(x).
Here, it is given that
p(x) is a polynomial with integer coefficients and p(-3) = 0.
Therefore, by Factor theorem, we can say that (x-(-3)), ie., (x + 3) is a factor of the polynomial p(x).
Thus, (x + 3) is a factor of the polynomial.
Option (A) is CORRECT.
