Factoring quadratics as (x+a)(x+b) | Mathematics II | High School Math | Khan Academy

Sal factors x²-3x-10 as (x+2)(x-5) using the sum-product form: (x+a)(x+b)=x²+(a+b)x+a*b.

High School Math on Khan Academy: Did you realize that the word "algebra" comes from Arabic (just like "algorithm" and "al jazeera" and "Aladdin")? And what is so great about algebra anyway? This tutorial doesn't explore algebra so much as it introduces the history and ideas that underpin it.

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[jenweatherwax]

I am so happy I could cry, thank you for your help!

[TheLawrence]

This channel deserves Pewdiepie fame!!! Good Job! Really! One of the best channels on Youtube!

[geoffhut]

Where did the other x go in the ax + bx when you (a+b)x … im guessing since they are times by the same x you only need one but it just doesn’t feel right to lose it without using it or am I misinterpreting this?

[zobayerzahid]

why doesn't this channel have 20m subs?

[krishnac]

x^2-3x-10 => x^2-5x+2x-10 => x(x-5)+2(x-5) => (x-5)(x+2)

[unrealdevop]

Not sure I like the idea of guessing what the numbers are. It doesn't feel right to have something like this where you have to solve an equation by process of elimination....is there no mathematical way to solve these types of questions?
There may be situations where the numbers aren't single digit numbers....am I supposed to then just brainstorm over what 'a' and 'b' equal? Surely there is a better way to do this. It seems like really bad practice to do things in such a manner.

It's like in programming when people use Magic Numbers without bothering to explain what they represent....then at some point someone else has to fix a bug but they are going through your code and they come across it and have to spend a stupid amount of time just puzzling over what the value represents. If things aren't properly explained they cost people valuable time.

[akatsuki]

I'm sorry, but this isn't right. It doesn't obey the Girard Relations of sum and product.