# Quick Math Factorization- Factorization

## quick math factorization

1
##### 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 $$(x + 2)(x + 3)$$.