factorization

The notes, dated May 19, 2025, describe the factorization of quadratic trinomials, which are expressions in the form x² + bx + c. The notes explain that there are two types to factorize:

Type 1: x² + bx + cType 2: x² ± bx - c

The focus is on factorizing the first type, x² + bx + c. The key concept is that if the sum in the trinomial is positive, then the signs within the brackets of the factored form will be the same.

Examples:

x² + 7x + 6 = (x + 6)(x + 1)x² - 9x + 20 = (x + 3)(x + 6)

In the first example, to factor x² + 7x + 6, find two numbers that add up to 7 and multiply to 6. These numbers are 6 and 1, so the factored form is (x + 6)(x + 1). The note incorrectly factors x² - 9x + 20. The correct factorization is (x - 4)(x - 5). The two numbers should add up to -9 and multiply to 20, which are -4 and -5.

In general, when factoring x² + bx + c:

Find two numbers that add up to b and multiply to c.Use these numbers to create two binomials in the form (x + number 1)(x + number 2).