Factor completely: 50x³ − 18x. (Section 5.5, Example 2)

Question

Accepted Answer

Hello, today we're gonna be completely factoring the given expression. So what we are given is 36 r cubed -100 r. Now, before we factor this given expression, let's go ahead and factor out a greatest common factor from the given expression. So taking a look at the coefficients 36 and 136 and 100 share a common multiple of four. So we can go ahead and factor out a four from the given expression. Furthermore, there's at least one R term in each of the given terms. So we can also factor out an R from the given expression. So if we factor out four R from the given expression, we can go ahead and rewrite this as four R times the quantity nine R squared minus and nine are squared can be rewritten as three R times three R and that itself can be simplified as three R squared. Furthermore, 25 is a perfect square because it could be rewritten as five times five, which itself can be simplified as five squared. So we can rewrite the current expression as four R times the quantity three R squared minus five squared. And what we have here is a difference of squares when we want to factor a difference of squares, the difference of square states that if you have the quantity in the form A squared minus B squared, this can be factored as A plus B times the quantity A minus B. Here, we're going to let A equal to three R and we're going to let B equal to five. So if we factor this, using the difference of squares, we can rewrite three R squared minus five squared as A plus B, which is going to be three R plus five times A minus B, which is going to be three R minus five. And keep in mind that we factored out A four R in the beginning. So we're going to include that factor in front of our groups, which is going to give us four R times the quantity three R plus five times the quantity three R minus five. And this is going to be the completely factored version of our given expression. And with that being said, the answer to this problem is going to be D. 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.

Factor completely: 50x³ − 18x. (Section 5.5, Example 2)

Key Concepts

Factoring Polynomials

Greatest Common Factor (GCF)

Difference of Squares

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