P(x) is a polynomial with integer coefficients and p(-3) = 0. Which statements must be true? Choose all that apply.

[tex]P(x) is a polynomial with integer coefficients and p(-3) = 0. Which statements must be true? Choo[/tex]

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P(x) is a polynomial with integer coefficients and p(-3) = 0. Which statements must be true? Choose all that apply.

[tex]P(x) is a polynomial with integer coefficients and p(-3) = 0. Which statements must be true? Choo[/tex]

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.

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.

1.)If f(a) = 0, then x - a is a factor of the polynomial.

2.) x + 3 is a factor of the polynomial.

Your answer is the first option, (x + 3) is a factor of the polynomial.

We know this from the factor theorem, which states that if f(a) = 0, then (x - a) is a factor.

Thus we know that (x - -3) is a factor, which simplifies to (x + 3).

All the other answer options do not have to be true, because (x - 3) doesn’t have to be factor, -3 doesn’t have to be the constant of the polynomial, and p(x) can have any number of linear factors, which means the only answer you should select as definitely true is the first option.

I hope this helps! Let me know if you have any questions 🙂

x+3 is a factor of P

Step-by-step explanation:

By the factor theorem:

P(a)=0 <-> x-a is a factor of P.

You have P(-3)=0.

This implies x-(-3) is a factor of P.

Note: x-(-3)=x+3.

yes all that apply to this q9