Quadratic expressions are of the form ax² + bx + c, where a, b, c are real numbers. You can see that the quadratic algebraic expression of the form ax² + bx + c has three terms and the highest exponent of the variable is 2.

Factorizing the quadratic expression of the form ax² + bx + c means re writing it as a product of its two linear factors of the form a (x + p)(x + q)

Case i. When a = 1
ax² + bx + c = x² + bx + c
Rewrite x² + bx + c as a product of its linear factors of the form (x + p)(x + q)
x² + bx + c = (x + p)(x + q)
x² + bx + c = x(x + q) + p(x + q)
x² + bx + c = x² + qx + px + pq
x² + bx + c = x² + (p + q)x + pq

The left and right sides will be equal if b = p + q and c = pq. This means, if we can get two number p and q such that their sum is equal to b and their product equal to c, we can easily factorize x² + bx + c as (x + p)(x + q)