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Middle/High School Algebra, Geometry, and Statistics (AGS)
Factorization of any Quadratic Polynomial - I

Method of Factorization:

1. Multiply the coefficient of x2 by the constant term.

2. Resolve this product into two factors such that their sum is the coefficient of x.

3. Rewrite the x term as the term of two terms with these coefficients.

4. Then we can find the factors.

Factorize, 6x2+19x+15.

Given that, 6x2+19x+15.
Here x2 coefficient is 6 and constant term is 15,
the product of these terms is = 6 * 15 = 90
19 = 10 + 9 = 10 * 9 = 90.
Therefore, 6x2+19x+15 = (6x2+10x)+(9x+15).
Take 2x and 3 as common, we get
= 2x(3x+5)+3(3x+5)
Take (3x+5) as common, we get
= (3x+5)(2x+3)

Directions: Solve the following problems. Also write at least ten examples of your own.