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Factoring polynomials with four or more terms can be more complex than factoring binomials or trinomials. However, there are strategies that can help simplify the process.

Step-by-Step Process

To factor polynomials with four or more terms, follow these steps:

1. Group the terms in pairs.
2. Factor each pair using common factoring techniques such as GCF, difference of squares, or trinomial factoring.
3. Look for a common factor among the resulting expressions.
4. Factor out the common factor.
5. Express the polynomial as the product of the common factor and the remaining expressions.
6. Check your work by multiplying the factors to ensure you get the original polynomial.

Example

Let's factor the polynomial $$x^3+2x^2-3x-6$$:

Step 1: Group the terms - $$\left(x^3+2x^2\right)-\left(3x+6\right)$$.

Step 2: Factor each pair - $$x^2\left(x+2\right)-3\left(x+2\right)$$.

Step 3: Look for a common factor - Both expressions share $$\left(x+2\right)$$ as a common factor.

Step 4: Factor out the common factor - $$\left(x+2\right)\left(x^2-3\right)$$.

Step 5: The polynomial is now factored as $$\left(x+2\right)\left(x^2-3\right)$$.

Factoring polynomials with four or more terms requires practice and patience, but mastering this skill can greatly simplify algebraic expressions and equations.