Factor By Grouping Calculator Symbolab Calculus

Factoring by Grouping Method:

\[ \text{Given } ax^3 + bx^2 + cx + d \text{, group as } (ax^3 + bx^2) + (cx + d) \]

Factored Expression:

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1. What is Factoring by Grouping?

Factoring by grouping is a method used to factor polynomials that have four or more terms by grouping terms together that have common factors.

2. How Does Factoring by Grouping Work?

The method works by:

\[ \text{Grouping: } (ax^3 + bx^2) + (cx + d) \] \[ \text{Factoring each group: } x^2(a + b) + (c + d) \]

Where:

Look for common factors in each group
Factor out the GCF from each group
Look for a common binomial factor
Factor out the common binomial

3. Steps to Factor by Grouping

Step 1: Group terms with common factors
Step 2: Factor out the GCF from each group
Step 3: Identify and factor out the common binomial factor
Step 4: Verify by expanding the factored form

4. Using the Calculator

Tips: Enter a polynomial expression with 4 terms. The calculator will attempt to factor it by grouping.

5. Frequently Asked Questions (FAQ)

Q1: What types of polynomials can be factored by grouping?
A: Typically polynomials with four terms, but sometimes works with more.

Q2: Does the order of terms matter?
A: Sometimes rearranging terms can reveal factorable groups.

Q3: What if no common binomial factor appears?
A: Try different groupings or the polynomial may not be factorable by grouping.

Q4: Can this method factor all polynomials?
A: No, it's specific to certain forms. Other methods may be needed.

Q5: How is this different from other factoring methods?
A: It's specifically for polynomials where terms can be grouped into factorable pairs.