I need help on how to factor a polynomial by grouping
To factor a polynomial by grouping, follow these steps:
Step 1: Identify the polynomial and determine if it can be grouped.
Step 2: Group the terms of the polynomial into pairs or sets.
Step 3: Identify any common factors within each pair or set of terms.
Step 4: Factor out the common factors from each pair or set.
Step 5: Look for a common factor between the resulting terms and factor them out if possible.
Step 6: Combine the remaining factors to obtain the final factored form of the polynomial.
Let's illustrate this process with an example:
Example: Factor the polynomial 2x^3 + 4x^2 - 6x - 12.
Step 1: Identify and determine if it can be grouped. In this case, it can be grouped into pairs.
Step 2: Group the terms: (2x^3 + 4x^2) - (6x + 12).
Step 3: Identify common factors within each pair:
2x^2(x + 2) - 6(x + 2).
Step 4: Factor out the common factors:
2x^2(x + 2) - 6(x + 2).
Step 5: Look for a common factor between the resulting terms:
(x + 2)(2x^2 - 6).
Step 6: Combine the remaining factors:
(x + 2)(2(x^2 - 3)).
Therefore, the factored form of 2x^3 + 4x^2 - 6x - 12 is (x + 2)(2(x^2 - 3)).
By following these steps, you can factor a polynomial by grouping.