Question

P(x) is a polynomial with integer coefficients and p(3) = 0.

Answer 1

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.