Problem 105
Question
Suppose that a polynomial contains four terms and can be factored by grouping. Explain how to obtain the factorization.
Step-by-Step Solution
Verified Answer
To factorize a polynomial by grouping, we first group the terms in pairs. We then find the GCF in each group, and factor it out of each group, simplifying the expressions. Using the associative property, we observe that the simplified expressions from each group now have a common factor which we can factor out. The final result is the factorization of the original polynomial.
1Step 1: Grouping the Terms
We start by grouping pairs of terms. The common way to do this is in pairs that come next to each other, but this may change depending on the polynomial.
2Step 2: Factoring Common Terms
In each group that was identified in the first step, find the greatest common factor (GCF) and factor it out. Each group of terms should reduce to a simplified expression.
3Step 3: Associative Property
By examining the simplified expressions obtained in step 2, we should find that they now have a common factor. We factor this expression out using the associative property of multiplication.
Other exercises in this chapter
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