A very strange encounter. (1 Viewer)

[Gussy Booo]

Can someone please explain how to factorize this step by step. Also, is there a name for this process?

Completely Factorize:

5x² - 9xy -2y²

Thanksssssssssss:rofl:

 

[LordPc]

(5x-y)(x+2y)

guess and check
bit of reasoning.

you know it will be
(...x...y)(...x...y)
and you know there is atleast 1 "-" in there and you know the xy term is negative,
which indicates that the 5x will multiply a negative, so you get
(5x...y)(x - ...y)

so its down to a few options. you might be able to reason to the answer, but mentally you should be able to throw in numbers and see what works and what doesnt.

 

[Gussy Booo]

, yes. That is the answer. But there has to be a more suitable process. My friend showed me it, but I've forgotten. He mentioned something about PSF. It was quite interesting how he did it.

Next question:

Express -x²+2x+3 in the form -(x-a)²+b

Just steps on -how- to do it. Thanks !

 

[tommykins]

complete the square - or if ur lazy, equate them

-x^2 + 2x + 3 = -(x-a)^2 + b

expand rhs

 

[shady145]

psf = product sum factor... personally i think this process takes longer than is needed to factorise. i use the cross method... much faster
5x² - 9xy -2y²
product = first term multiply by the last term
P:-10x^2y^2
sum is the middle term
S: -9xy
factor is, what multiplies together to give P and add to give the S
F: -10xy, xy
now rewrite it... u replace the middle term with your F
5x² -10xy +xy -2y²
now take factors out of each
5x(x-2y) +y(x-2y)
(x-2y)(5x+y)
lol waste of time imo...
if i could draw crosses somehow i could show the cross method

 

[Drongoski]

Can someone please explain how to factorize this step by step. Also, is there a name for this process?

Completely Factorize:

5x² - 9xy -2y²

Thanksssssssssss:rofl:

But this is so basic; no need for any fancy approach.

Just start off with: (5x - ?y)(x - ?y)

The -2 coeff of y² term can only be -2 x 1 or -1 x 2 [for the 2 '?' ]

By inspection: you end up with (5x + y)(x - 2y) [not: (5x - y)(x + 2y) ]

ps: in writing out, I start off with '-' first and this can be easily changed into a '+' if reqd whereas I cannot change a '+' to a '-' without being messy.

 

[Xcelz]

, yes. That is the answer. But there has to be a more suitable process. My friend showed me it, but I've forgotten. He mentioned something about PSF. It was quite interesting how he did it.

The PSF method is a simple way to solve quadratics if you can't solve it in your head.

Take the equation: x^2+5x+6 (where a=1,b=5,c=6)
P: (product) you multiply 'a' and 'c'. result = 6.
S: (sum) you find the sum of 2 factors of 6 which give the value of 'b'. in this case +3,+2.
F: (factors/factorisation)
x^2+3x+2x+6 = 0
x(x+3)+2(x+3)=0
(x+2)(x+3)=0
x=-2 and -3.

hope that is what u want.

 

[addikaye03]

psf = product sum factor... personally i think this process takes longer than is needed to factorise. i use the cross method... much faster
5x² - 9xy -2y²
product = first term multiply by the last term
P:-10x^2y^2
sum is the middle term
S: -9xy
factor is, what multiplies together to give P and add to give the S
F: -10xy, xy
now rewrite it... u replace the middle term with your F
5x² -10xy +xy -2y²
now take factors out of each
5x(x-2y) +y(x-2y)
(x-2y)(5x+y)
lol waste of time imo...
if i could draw crosses somehow i could show the cross method

My teacher uses the cross method aswell... i'm not big on it personally. I'm a PSF supporter

 

[ninetypercent]

I'm a PSF supporter too