Factor The Following Four Term Polynomial by Grouping Calculator

How to Use This Calculator

To use the polynomial grouping factoring calculator:

1. Enter the coefficients for each term of your four-term polynomial in the input fields provided.
2. Click the "Calculate" button to factor the polynomial by grouping.
3. Review the factored form of the polynomial displayed in the results section.
4. If needed, use the "Reset" button to clear the inputs and start over.

The calculator will show you the step-by-step process of factoring by grouping, including the common factors found and the final factored form.

How Polynomial Grouping Factoring Works

Factoring by grouping is a method used to factor polynomials that have four terms. The process involves:

1. Grouping the first two terms and the last two terms together.
2. Factoring out the greatest common factor (GCF) from each group.
3. Factoring out the common binomial factor from the resulting expression.

For example, consider the polynomial 2x² + 4x + x + 2. We can factor by grouping as follows:

1. Group the first two terms and the last two terms: (2x² + 4x) + (x + 2)
2. Factor out the GCF from each group: 2x(x + 2) + 1(x + 2)
3. Factor out the common binomial factor: (2x + 1)(x + 2)

Worked Examples

Example 1: Factoring 6x² + 9x + 3x + 4.5

1. Group the terms: (6x² + 9x) + (3x + 4.5)
2. Factor out the GCF from each group: 3x(2x + 3) + 1.5(2x + 3)
3. Factor out the common binomial factor: (3x + 1.5)(2x + 3)

Example 2: Factoring x³ + 2x² + x + 2

1. Group the terms: (x³ + 2x²) + (x + 2)
2. Factor out the GCF from each group: x²(x + 2) + 1(x + 2)
3. Factor out the common binomial factor: (x² + 1)(x + 2)