Factoring by Grouping

Factoring by grouping is a method used to factor polynomials with four terms. The basic idea is to group the terms in pairs and factor out a common factor from each pair. Then, factor out the common binomial factor from the resulting terms to obtain the final factored form.

Step-by-Step Process for Factoring by Grouping:

1. Write down the polynomial: Start with the given polynomial expression.
2. Group the terms: Group the terms in pairs such that the first pair shares a common factor and the second pair also shares a common factor.
3. Factor out the common factors: Factor out the common factors from each pair of terms separately.
4. Factor out the common binomial factor: Factor out the common binomial factor from the resulting terms.
5. Write the final factored form: Write the final factored form as the product of the two binomial factors.

Example:

Let's illustrate the process with an example. Consider the polynomial:

4x + 8 + 3x + 6

Step 1: Write down the polynomial:

4x + 8 + 3x + 6

Step 2: Group the terms:

(4x + 8) + (3x + 6)

Step 3: Factor out the common factors:

4(x + 2) + 3(x + 2)

Step 4: Factor out the common binomial factor:

(x + 2)(4 + 3)

Step 5: Write the final factored form:

(x + 2)(7)

So, the final factored form of the given polynomial is (x + 2)(7).

Study Guide:

When factoring by grouping, it's important to look for common factors within pairs of terms. Here are some key points to remember when using this method:

• Always look for common factors within pairs of terms.
• Group the terms in such a way that each pair shares a common factor.
• Factor out the common factors from each pair of terms.
• Factor out the common binomial factor from the resulting terms.
• Check the final factored form by multiplying the binomial factors to ensure it equals the original polynomial.

Practice factoring by grouping with various examples to strengthen your understanding of this method.

Hope this study guide helps! Good luck with factoring by grouping!