Answer:
The answer is below
Step-by-step explanation:
P(x) is a polynomial with integer coefficients and p(-3) = 0.
Which statements must be true? Choose all that apply.
x + 3 is a factor of the polynomial.
x - 3 is a factor of the polynomial.
-3 is the constant term of the polynomial.
p(x) can have at most 3 linear factors.
Solution:
Polynomial is an expression composed of variables, constants and exponents linked together by mathematical operations (addition, subtraction, multiplication and division)
Given that:
p(-3) = 0.
Since P(-3) = 0, this means that -3 is a factor of the polynomial. Hence:
The factor theorem states that states that if f(a) = 0, therefore a is a factor of the polynomial and hence (x - a) is a factor of polynomial f(x).
Therefore using the factor theorem, we get that x + 3 is a factor of the polynomial.
