Factoring Polynomials: Solving x² - 5x + 6

To factor a polynomial like $x^2 - 5x + 6$, we need to find two numbers that multiply to the constant term (in this case, 6) and add up to the coefficient of the middle term (in this case, -5).

In this example, the numbers are -2 and -3, since $-2 \times -3 = 6$ and $-2 + (-3) = -5$.

So, we can rewrite the polynomial as $(x - 2)(x - 3)$.

This method, known as factoring by grouping, helps us solve quadratic equations and understand the behavior of parabolas. Mastering this skill is essential for further studies in algebra and mathematics.