Factorising non-monic quadratic equations (1 Viewer)

[Joshmosh2]

Greetings, are there any tricks to determine how to factor non-monic quadratic equations?
for example, what would be the common thought process to factor something like
y = 6x^2-5x+1

Thanks in advance

 

[randomly_generated]

Nor really, just practice. I can see you will have to rewrite it as 6x^2 -6x + x + 1 because I've done so many of them

 

[Drongoski]

Well you can try out the initial frameworks:

= (6x - ? )(x - ?) or

= (3x - ?)(2x - ?)

The 1st one obviously wont do, so you try the only other one.

 

[Stygian]

Greetings, are there any tricks to determine how to factor non-monic quadratic equations?
for example, what would be the common thought process to factor something like
y = 6x^2-5x+1

Thanks in advance

essentially inspection just like you would for monic ones albeit with slightly messier numbers at times

 

[enigma_1]

just use quadratic formula

 

[Stygian]

just use quadratic formula

I would only use this for factorisation if worst comes to worst you can't get it by other means, otherwise inspection is usually faster and more efficient

 

[faisalabdul16]

y = 6x^2-5x+1

So I would add the constant for x^2 and the final constant, i.e. 6 x 1 =6

Then I know that I need two numbers which will multiply to give me 6, and add to give me -5 (constant in front of x)

You basically just think through factors: -3 and -2 seems to do it

Then you split the constant in front of x into these two factors, i.e.

y= 6x^2 - 3x - 2x + 1

Now you can factorise:

y = 3x(2x -1 ) - 1(2x-1)
i.e. = (3x-1)(2x-1)

Hope that makes sense haha. Its a lengthy process (this method is anyway), but once you practice enough, it will be faster than the cross-method (which relies on trial and error)

Best way to do it, if one is unable to do it by inspection

 

[faisalabdul16]

Over time the inspection becomes intuitive. I started doing it this way and I think with time speed develops and your mind programs it to make it intuitive

yeah that is true. Over time you just become accustomed to the process and really quick with it.

 

[BLIT2014]

https://www.youtube.com/watch?v=7fK...j3DeykJmI&annotation_id=annotation_1753188209