## quick math factorization

##### Enter expression in this form

Example: 3x^2 + 9x

### Factorization

Factorization is the process of breaking down an algebraic expression into a product of simpler expressions, or factors, which when multiplied together give the original expression. This is a crucial skill in algebra, as it simplifies expressions and solves equations more easily.

#### Types of Factorization

**1. Common Factor**: Taking out the greatest common factor (GCF) from terms.**2. Difference of Squares**: Expressions in the form \(a^2 – b^2\), which factorizes to \((a – b)(a + b)\).**3. Quadratic Trinomials:** Quadratics in the form \(ax^2 + bx + c\), which factorize to \((mx + n)(px + q)\).**4. Perfect Square Trinomials:** Expressions like \(a^2 + 2ab + b^2\), which factorize to \((a + b)^2\).

#### Detailed Example

Let’s factorize the quadratic expression \(x^2 + 5x + 6\).

**Steps**:

1. Identify the coefficients:

– Here, \(a = 1\), \(b = 5\), and \(c = 6\).

2. Find two numbers that multiply to \(c\) (constant term) and add up to \(b\) (coefficient of \(x\)):

– We need two numbers that multiply to \(6\) and add to \(5\).

– These numbers are \(2\) and \(3\) because \(2 \times 3 = 6\) and \(2 + 3 = 5\).

3. Write the expression in factored form using the two numbers found:

– \(x^2 + 5x + 6\) can be written as \((x + 2)(x + 3)\).

4. Verify by expanding:

– Multiply the factors to ensure they give the original expression:

\[(x + 2)(x + 3) = x(x + 3) + 2(x + 3)\]

\[= x^2 + 3x + 2x + 6\]

\[= x^2 + 5x + 6\]

The original expression \(x^2 + 5x + 6\) is correctly factorized as \((x + 2)(x + 3)\).