Video: Factorizing Algebraic Expressions by Grouping

Factor the expression 𝑥²(2𝑥 + 5) + 2𝑥 + 5 completely.

01:11

Video Transcript

Factor the expression 𝑥 squared times two 𝑥 plus five plus two 𝑥 plus five completely.

Here it seems that it’s beginning of factoring by grouping. So notice that the two 𝑥 plus five and the two 𝑥 plus five actually match. And when we factor by grouping, we want that to happen.

So when we factor by grouping, we group the first two terms together and the last two terms together and we take out a GCF of both. And notice, there’s already a GCF taken out of the first set of parentheses, the 𝑥 squared.

Now for the second set of parentheses, which we’ve added here, we want to take out the GCF of two 𝑥 and five. And the only number that can come out of two 𝑥 and five would be one. And this is good because we want the parentheses to match, and they do.

So the GCFs will come together to make one factor. And then the matching parentheses, the two 𝑥 plus fives, will come together to be the other factor.

Therefore, after factoring completely, we get an answer of 𝑥 squared plus one times two 𝑥 plus five.

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