In Exercises 95–104, factor completely.

0.04x² + 0.12x + 0.09

Question

In Exercises 95–104, factor completely.

0.04x² + 0.12x + 0.09

Accepted Answer

Hello. Today we're gonna be completely factorizing the following polynomial. So what we are given is 0.25 Y squared plus 0.7 Y plus 0.49. Now the one property that's gonna help us factor, this is the property of A plus B squared. See A plus B squared can be expanded to give us a squared plus two times A times B plus B squared. And if we look at the current polynomial, we can actually rewrite the given polynomial in the form of A squared plus two A B plus B squared. If we look at the first term, which is 0.25 Y squared, 0.25 Y squared can be rewritten as 0.5 Y times 0.5 Y which itself can be rewritten as 0.5 Y squared. The middle term 0.7 Y can be rewritten as two times 0.35 Y. And the last term, 0.49 can be rewritten as 0. times 0.7, which itself can be rewritten as 0.7 squared. So if we replace each term with the terms that we just came up with right now, we can rewrite the original polynomial as 0. Y squared plus two times 0. Y Plus 0. 0.7 Squared. And this matches the form of A squared plus two A B plus B squared. So we can go ahead and rewrite this as 0. Y plus 0.7 squared, which is going to be the factored form of the given polynomial. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 95–104, factor completely. 0.04x² + 0.12x + 0.09

Key Concepts

Factoring Quadratic Expressions

Common Factor Extraction

Perfect Square Trinomials

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