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In $27-39,$ factor each polynomial completely.$$2 x^{3}+13 x^{2}+15 x$$

$x(x+5)(2 x+3)$

Algebra

Chapter 1

THE INTEGERS

Section 6

Factoring Polynomials

The Integers

Equations and Inequalities

Polynomials

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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02:15

In $27-39,$ factor each po…

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01:28

00:54

Factor each polynomial com…

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Factor each polynomial.

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so he wants a factor. This polynomial completely. So the first thing I notice is that we have a common Manami o of X here, here, in here. So I want a background in X. And whenever we backed out of mono meal, we always factor out the lowest degree. So in this case, just exit the first, which is just six. So they will have two x squared less 13 x plus 15 left. So now we can factor what's inside the parentheses. So we're gonna take this first term coefficient multiplying bar last time in two times 50 will give us 30. And we wanted to add to our middle term in this case, 13. So the list the factors of 31 in 30 soon scene three in tune and five and six because this 13 is positive. All both of the terms in the payer has to be positive. So this is our question, because one place starting starting line two plus 15 is 17 but three plays tennis 13 So that gives us the pier that we need. It's analogous. Split apart on middle turn. So we still have X, and they will have. I'm gonna use big markets here, but they will have two x squared and we split apart of mental term. So plus 10 IX, close three X and then bring known at plus 15 here to know any degree barbers to terms and then grouper Last two terms. So he's back throughout from our first factor. We can factor out too, because God is coming back to between suing San is too. They're looking also back to our necks. Cyril it with six plus five on the inside. From the second factor, we can factor out of three really put expose five on the inside. So now we'll have X. And because we have the same term here in here, we know that explosive five is a factor and they will bring down what's left to explosive three and we factor in complete

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