### Definition of Factors

Factoring a polynomial involves finding the quantities that, when multiplied together, produce the original polynomial. Factors are numbers or expressions that divide evenly into a given number or expression.

### Key Facts

- Definition of Factors:
- When factoring a polynomial, you are trying to find the quantities that you multiply together to create the polynomial.
- Factors are the numbers or expressions that divide evenly into a given number or expression.

- Greatest Common Factor (GCF):
- The GCF for a polynomial is the largest monomial that is a factor of each term in the polynomial.
- The GCF must be a factor of every term in the polynomial.
- Finding the GCF involves identifying the highest power of each variable that appears in all the terms.

- Process of Factoring Using GCF:
- Find the GCF of all the terms in the polynomial.
- Express each term as a product of the GCF and another factor.
- Use the distributive property to factor out the GCF.

- Examples:
- Example 1: Factoring Using the GCF
- Polynomial: 6x^2 + 9x
- GCF: 3x
- Factored form: 3x(2x + 3)

- Example 2: Factoring Polynomials
- Polynomial: 12x^3y^2 + 8xy^3
- GCF: 4xy^2
- Factored form: 4xy^2(3x^2 + 2y)

- Example 3: Factoring Polynomials
- Polynomial: 15a^2b – 10ab^2
- GCF: 5ab
- Factored form: 5ab(3a – 2b)

- Example 1: Factoring Using the GCF

### Greatest Common Factor (GCF)

The GCF of a polynomial is the largest monomial that is a factor of every term in the polynomial. The GCF must be a factor of every term in the polynomial. To find the GCF, identify the highest power of each variable that appears in all the terms.

### Process of Factoring Using GCF

- Determine the GCF of all the terms in the polynomial.
- Express each term as a product of the GCF and another factor.
- Use the distributive property to factor out the GCF.

### Examples

## Example 1: Factoring Using the GCF

- Polynomial: 6x^2 + 9x
- GCF: 3x
- Factored form: 3x(2x + 3)

## Example 2: Factoring Polynomials

- Polynomial: 12x^3y^2 + 8xy^3
- GCF: 4xy^2
- Factored form: 4xy^2(3x^2 + 2y)

## Example 3: Factoring Polynomials

- Polynomial: 15a^2b – 10ab^2
- GCF: 5ab
- Factored form: 5ab(3a – 2b)

### Sources

- Factoring Polynomials Using the GCF
- Factoring Polynomials Using the Greatest Common Factor (GCF)
- Factor Out GCF Calculator

## FAQs

### What is factoring by GCF?

Factoring by GCF involves finding the greatest common factor (GCF) of all the terms in a polynomial and then expressing each term as a product of the GCF and another factor. The GCF is then factored out using the distributive property.

### How do I find the GCF of a polynomial?

To find the GCF of a polynomial, identify the highest power of each variable that appears in all the terms. The GCF is the product of these highest powers.

### When can I use factoring by GCF?

Factoring by GCF can be used when every term in the polynomial has a common factor.

### What are the steps for factoring by GCF?

- Find the GCF of all the terms in the polynomial.
- Express each term as a product of the GCF and another factor.
- Use the distributive property to factor out the GCF.

### Can I factor any polynomial using GCF?

No, factoring by GCF is only possible when every term in the polynomial has a common factor.

### What are some examples of factoring by GCF?

- 6x^2 + 9x = 3x(2x + 3)
- 12x^3y^2 + 8xy^3 = 4xy^2(3x^2 + 2y)
- 15a^2b – 10ab^2 = 5ab(3a – 2b)

### What are the benefits of factoring by GCF?

Factoring by GCF can simplify polynomials, make them easier to solve, and reveal important properties of the polynomial.

### What are some common mistakes to avoid when factoring by GCF?

- Not finding the GCF correctly
- Not expressing each term as a product of the GCF and another factor
- Not using the distributive property correctly