What are the factors of the polynomial X² - 6X + 5?

What are the factors of the polynomial X² - 6X + 5?

• A. X - 5, X - 2
• B. X - 4, X - 1
• C. X - 5, X - 1
• D. X + 5, X + 1

Answer: (C)

To determine the factors of the polynomial \(X^2 - 6X + 5\), we can use the method of factoring by searching for two numbers that multiply to the constant term (5) and add to the linear coefficient (-6). The factors of 5 that can achieve this are -5 and -1 because: - When you multiply -5 and -1, you get: \[ -5 \times -1 = 5 \] - When you add -5 and -1, you get: \[ -5 + (-1) = -6 \] This satisfies both conditions required for factoring the polynomial. Thus, the polynomial can be factored as: \[ (X - 5)(X - 1) \] Choosing the correct answer involves recognizing that these two factors, \(X - 5\) and \(X - 1\), are what you get from the proper factoring of the polynomial. Therefore, the factors of \(X^2 - 6X + 5\) are accurately represented by \(X - 5\) and \(X - 1\).

To determine the factors of the polynomial (X^2 - 6X + 5), we can use the method of factoring by searching for two numbers that multiply to the constant term (5) and add to the linear coefficient (-6).

The factors of 5 that can achieve this are -5 and -1 because:

• When you multiply -5 and -1, you get:

[

-5 \times -1 = 5

]

• When you add -5 and -1, you get:

[

-5 + (-1) = -6

]

This satisfies both conditions required for factoring the polynomial.

Thus, the polynomial can be factored as:

[

(X - 5)(X - 1)

]

Choosing the correct answer involves recognizing that these two factors, (X - 5) and (X - 1), are what you get from the proper factoring of the polynomial. Therefore, the factors of (X^2 - 6X + 5) are accurately represented by (X - 5) and (X - 1).