Which of the following is a factor of the polynomial x² - 5x + 6?

To determine if a given expression is a factor of the polynomial ( x^2 - 5x + 6 ), we can use the factorization approach. This polynomial is a quadratic, and we are looking for two binomials that multiply to this expression.

The polynomial ( x^2 - 5x + 6 ) can be factored by finding two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of the ( x ) term). The numbers -2 and -3 meet these criteria because:

• ((-2) \cdot (-3) = 6)
• ((-2) + (-3) = -5)

Thus, we can express the quadratic polynomial as:

[ (x - 2)(x - 3) ]

From this factorization, we can see that ( x - 2 ) and ( x - 3 ) are the factors of the polynomial.

Now, when identifying if ( x - 2 ) is indeed a factor, we can see that it is present in the factorization. This confirms that it divides the polynomial evenly.

Although ( x - 3 ) is also a