he table below shows values of a polynomial

Question

at different values of
.

x p(x)
–4 28
–3 12
–2 0
–1 –8
0 –12
1 –12
2 –8
3 0
4 12
Which of the following are factors of
? Select two that are correct.

A.

B.

C.

D.

E.

Answer 1

To determine which of the given options are factors of the polynomial \( p(x) \), we need to identify the roots of the polynomial. A polynomial \( p(x) \) has a root at \( x = r \) if \( p(r) = 0 \). This means \( (x - r) \) is a factor of \( p(x) \).

Looking at the values in the table, we observe the following where \( p(x) = 0 \):

• \( p(-2) = 0 \)
• \( p(3) = 0 \)

Since the polynomial has roots at \( x = -2 \) and \( x = 3 \), the factors corresponding to these roots are:

• \( (x + 2) \) for the root at \( x = -2 \)
• \( (x - 3) \) for the root at \( x = 3 \)

Thus, the correct options would include these two factors.

If you provide the specific options (A, B, C, D, E) that you would like me to evaluate, I can identify which two correspond to the factors \( (x + 2) \) and \( (x - 3) \).