How to Factor When a≠1

[tonyennis]

I like this guy. Calm, matter of fact, and to the point.

[mohammedyaser]

I really want to thank you so much for this method. It didn't just help me, but it also helped my math teacher to teach how to factor a trinomial when a=/=0 and now it's been much easier of all of us. Thanks again, you're a lifesaver.❤

[Steve]

A nice trick, but it requires that the students do things with no good mathematical basis, e.g., taking a denominator (such as 2) and "just move it to the front as the coefficient of x."

[chocolateangel]

This method is often referred to as "Bottom's Up." I don't personally care for it because I find reducing things annoying. If I'm going to use a version of the AC method, I would rather use an area model.

[jamesharmon]

I LOVE this trick! Maybe SOME day I'll remember it! 😂

[FrogworfKnight]

Next time I am tutoring a student in this portion of Pre-Calc Algebra, I will be certain to keep this method in mind. Though they may still just resort to the quadratic formula, based on experience on trying to teach them other methods for quadratics whose leading coefficient isn't one.

[Yekemcar]

by those little tricks here and there, I re-discovering my love to maths again ❤
Thank you ..

[Lesly-icmq]

Thank you so much...
Can ...-4 ..and +3 help us obtain...the +x...in the middle???

[rainerzufall]

Warning: He said it, but this method does NOT always work!
At least, when he said in 0:32 "just for the convenience of it", it's crucial to reduce the fraction correctly. Because we multiflied the constant term by 6, this is mostly the case (but not always). If we don't reduce (or do it wrongly), we'd get 9/6 and 8/6 => (6 x + 9) (6 x - 8) = 36x² + 6x - 72, which is certainly not a factorization of 6x² + x - 12 (it's multiplied by 6). There's no real equation, if it depends on the reduction of fractions! Nice trick for usual constructed schoolbook questions with integer coefficients and/or solutions though.

[Inspire]

sir,
Please make videos on problems related to circles❤❤ because my geometry is not that good

[stevenpace]

Like many of his tricks, it is not transparent how it works. So here goes the explanation.
Moving the first coefficient to the last one is the same as dividing the first coefficient by 36, and the second by 6. The reason is that the whole expression equals zero, so you can multiply or divide all the coefficients by the same number without changing it. But what he did in the first operation DID change it, but in a useful way. It is like a substitution the first term is divided by 36, the coefficient of X squared, and second by six is the coefficient of X, and 36 is 6 squared. The method would be more transparent if you said u=X/6, and then you see the extra steps. Of course once you understand you can leave that out.

[davidlech]

You should be the head of our math department at UW Green Bay. So many students would benefit.

[Kenneth-gnnk]

In the second problem, what did he do with the 2 that was factored out???

[sakshamkumar]

Is it appilcable for constants in any form??

[vartanyegikyan]

Why you don't multiply x by 6 too? Can you explain, please?

[druariel]

6x12=72; 2x3x3x4= 9x-8x;
6x^2 +9x -8x -12
3x(2x+3)-4(2x+3)
(3x-4)(2x+3)
Just seeing if the method I use is faster and easier.
I am uncomfortable with the shown method because step 2 is not actually equivalent to the original although I see it all comes out to be the same

[ChavoMysterio]

6x²+x-12
6x²+9x-8x-12
3x(2x+3)-4(2x+3)
(3x-4)(2x+3) ❤

[AhoyYoutube]

How can you just take the 6 and multiply it by 12? And also, how can you take the denominator there at the end and just move it to be the coefficient? I’m confused on how mathematically it works.

[RobertKraig]

If only this shit existed when I was in school.

[pierrettebalazut]

Bonsoir,
Je n'ai pas très bien compris la simplification par 6 pour x?
6x^2+x-12
Comment on arrive à x^2+x+72?
Il y a quelque chose qui m'échappe !
On multiplie 12par 6, ce qui fait 72,
On divise 6x^2 par 6, ce qui donne x^2
Attendez: on a

Soit en simplifiant
x^2+(6/6)x-72/6
x^2+x-72/6
Soit (x+9/6)(x-8/6)
Soit (x+3/2)(x-4/3)
Ok j'ai compris !
MERCI
Ça y est