Welcome to solving a quadratic by factoring.

Carter is solving this equation by factoring.

Let's solve some quadratic equations by factoring.

That's the whole point of factoring by grouping.

lot of factoring examples.

This is hard using factoring.

For example, factoring quadratics with

And we're done factoring it.

Let me do the first step by hand and rewrite σ² by factoring out the square.

This is just factoring a quadratic.

So what I'm going to teach you is a technique called, factoring by grouping.

So, you might say, hey, why did we ever do that factoring by grouping?

This is a hard problem with factoring.

We can solve this without factoring it.

This isn't any kind of fancy factoring.

The Estonians are beating us at factoring polynomials?

Let's just finish factoring it since we started it.

So it's, it's really a decomposition of factoring problem.

And it's very hard to imagine factoring this quadratic.

In this video, I want to focus on a few more techniques for factoring polynomials.

You're probably not used to factoring out an entire binomial.

So this is super hard to do just using factoring.

You're not factoring in the tax deductions of mortgages, et cetera, of interest on your mortgage.

And so if you need cash, factoring is a normal part of financing in certain industries ???

Let's say you're me and you're in math class and you're supposed to be learning about factoring.

You might want to review factoring polynomials if that doesn't look familiar.

So that's why this whole factoring by grouping even works, or how we're able to figure out what a and b even are.

And here, this would be just a traditional factoring problem, the type that we've seen in the last few videos.

They're getting more help on the basics of solving equations, factoring quadratics, graphing parabolas.

Now what's useful about this and this is why we call it factoring by grouping is we can see, are there any common factors in these first two terms right over here?

Might want to review factoring a polynomial, if you found that a little confusing, that step.

Maybe when we were doing the factoring problems we didn't realize graphically what we were doing.

And normally when we're factoring, especially when we're beginning to factor, we're dealing with integer numbers.

I don't want this to ruin all of the training you've gotten on factoring so far.

In this video I want to do a bunch of examples of factoring a second degree polynomial, which is often called a quadratic.

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It was a minus here, but I'm factoring out of a minus e to the minus st.

I think at this point you're ready to try some solving quadratics by factoring and I'll do a couple more modules as soon as you get some more practice problems.

So we're literally just factoring out a 2x plus 5, and we're left with an x plus 6.

So you get vb minus vc times time I'm just factoring out the time is equal to 300.

You could try to factor it, but personally I don't enjoy factoring things when I have a coefficient.

So one possibility is that cryptographic protocols, so things were keeping secrets in encrypting data that are based on problems like factoring that are in NP could be cracked.

Now, I'm going to close up with something slightly different, but just to make sure that you have a well rounded education in factoring things.

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In position. Standing by.