Understanding how factorization connects to the roots of polynomials is very important in math, especially in A-Level Mathematics.

When you factor a polynomial, you break it down into simpler parts, and this helps you find its roots.

Example:

Let’s look at the polynomial ( P(x) = x^2 - 5x + 6 ).

1. Finding Roots: To find the roots, we set ( P(x) = 0 ).
2. Factorization: It can be factored into ( (x - 2)(x - 3) ). This shows that the roots are ( x = 2 ) and ( x = 3 ).

Techniques:

• Synthetic Division: This method makes it easier to find factors. For example, if we want to check if ( x - 2 ) is a factor, we can use synthetic division to divide ( P(x) ) by ( x - 2 ).

Knowing how to connect factorization and roots will help you solve polynomials better and get ready for more advanced algebra topics!