Question

If p(3) = 0 for polynomial p(x), state one factor of p(x)​

Answer 1

Answer:

(x - 3) is one of the factors.

Step-by-step explanation:

as x=3 is a zero then x-3 is a factor

Answer 2

Given,

For a polynomial p(x), p(3) = 0.

To find,

One factor of p(x).

Solution,

It is given that p(x) is a polynomial. Also, the polynomial p(x) has a value of 0, at the value of x = 3.

Mathematically,

p(3) = 0, for the given polynomial p(x).

Since zero of a polynomial is one at which the value of the polynomial is 0.

It means, 3 is a zero of the given polynomial p(x).

Now, a factor of the polynomial can be found by equating the variable to the zero of the polynomial and then making the equation such that the variable and its value (that is zero of the polynomial) is on the same side. So, here,

x = 3

⇒ (x - 3) = 0.

Therefore, (x - 3) is a factor of the given polynomial p(x).