Question

Consider the polynomial function P (x) = x^3 - 4x^2 + x+ 6.
• P(-1) = 0
• P (2) = 0
• P(3) = 0

Which three expressions are factors of P (x)?
A. (x + 1)
B. (x +2)
c. (x+ 3)
D. (X-1)
E. (x-2)
F. (x- 3)

Answer 1

Since \( P(-1) = 0 \), it means that \( x = -1 \) is a root of the polynomial, so \( (x + 1) \) is a factor of \( P(x) \).

Since \( P(2) = 0 \), it means that \( x = 2 \) is also a root of the polynomial, so \( (x - 2) \) is a factor of \( P(x) \).

Since \( P(3) = 0 \), it means that \( x = 3 \) is another root of the polynomial, so \( (x - 3) \) is a factor of \( P(x) \).

Thus, the three expressions that are factors of \( P(x) \) are:

A. \( (x + 1) \)
E. \( (x - 2) \)
F. \( (x - 3) \)

So the answer is A, E, and F.