Quadratics help

i got 2 questions that im stuck on, please tell me the method, i can use that then to find the answer. put the answer in the spoiler if u want so i can compare perhaps :biggrin:

Factorise 2x^2 - 11xy + 5y^2

i've never came across this type before

and also

simplify expression, leave answer in factorised form

x^2 + 4x + 3
----------------
x + 1

thank you!

(edited 8 years ago)

Reply 1

16Characters....

For the first don't be thrown off by the y's. Just go about it like an ordinary quadratic. Not really sure how other to explain this than by an example. Consider

x^2 + 2xy + y^2

. We are just going to treat it as a normal quadratic and so we want to find two numbers which multiply to give y^2 and sum to give 2y. y and y satisfy this. Hence

x^2 + 2xy + y^2 = (x+y)(x+y) = (x+y)^2

. Now try it with your's.

For the second, assuming it is meant to be

\frac{x^2 + 4x + 3}{x+1}

then factorise the numerator.

(edited 8 years ago)

Reply 2

TSR George

Original post by 16Characters....

For the first don't be thrown off by the y's. Just go about it like an ordinary quadratic. Not really sure how other to explain this than by an example. Consider

x^2 + 2y + y^2

. We are just going to treat it as a normal quadratic and so we want to find two numbers which multiply to give y^2 and sum to give 2y. y and y satisfy this. Hence

x^2 + 2y + y^2 = (x+y)(x+y) = (x+y)^2

. Now try it with your's.

For the second, assuming it is meant to be

\frac{x^2 + 4x + 3}{x+1}

then factorise the numerator.

sooo sorry, i meant 11xy but other than that i understand your explanation thank you

Reply 3

16Characters....

It's OK, I meant 2xy in my example too whoops.

Reply 4

under8ed

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

use AC method

Reply 5

TSR George

Original post by under8ed

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

use AC method

what is AC method?

Reply 6

under8ed

The method you use to solve quadratics, i suspect you do this without realising

https://people.richland.edu/james/misc/acmeth.html

This simplifies it, take the 'a' to equal 2 and the 'c' to equal 5

Reply 7

gapyear2018

Original post by 16Characters....

It'is OK, I meant 2xy in my example too whoops.

Attachment not found

Hope this helps slightly, not sure if it's the AC method but it's what I do.

Original post by ScienceFantatic

Attachment not found

Hope this helps slightly, not sure if it's the AC method but it's what I do.

I know how to factorise a quadratic, I do not however know how to proofread. You may wish to quote the OP here instead of me...

Edit: Though thank you for trying to help out.

(edited 8 years ago)

Reply 9

gapyear2018

Original post by 16Characters....

I know how to factorise a quadratic, I do not however know how to proofread. You may wish to quote the OP here instead of me...

Edit: Though thank you for trying to help out.

You're right I did quote the wrong person, sorry!

Reply 10

TSR George

Original post by ScienceFantatic

You're right I did quote the wrong person, sorry!

@ihatePE

oh thanks! i'll use this for other questions i have now

Reply 11

TeeEm

Original post by under8ed

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

use AC method

Reply 12

under8ed

Original post by TeeEm

I didnt realise other people arent taught this, its just a logical way of solving a quadratic

Reply 13

TeeEm

Original post by under8ed

I didnt realise other people arent taught this, its just a logical way of solving a quadratic

What school year are you in?

Reply 14

Louisb19

If you can't see it intuitively maybe then set

y = c

(c is a constant) and notice (hopefully) how this can be factorised in the normal way :smile:

Reply 15

under8ed

Original post by TeeEm

What school year are you in?

yr 11

Reply 16

TeeEm

Original post by under8ed

yr 11

No worries ... some teachers teach some very exotic approaches
For most students which take maths beyond GCSE, factorizing a quadratic requires no particular method.

All the best!