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How to factorise a quadratic when the co-efficient of X isn't 1.

I've been given 2x^2 +5t +2 to factorise but I can't seem to do it. I normally use the method where you find 2 numbers which add to make the 2nd number and multiply to make the 3rd number but I can't make that work here.
Reply 1
Avatar for joostan
joostan
13
Original post by AxSirlotl
I've been given 2x^2 +5t +2 to factorise but I can't seem to do it. I normally use the method where you find 2 numbers which add to make the 2nd number and multiply to make the 3rd number but I can't make that work here.


Assuming that's 2x2+5x+22x^2+5x+2, write two brackets (2x+a)(x+b)(2x+ a)(x+b).
You can work out what aa and bb are from there.
Alternatively, you could write 2x2+5x+2=2(x2+52x+1)2x^2+5x+2=2(x^2+\frac{5}{2}x+1) and factorise the (x2+52x+1)(x^2+\frac{5}{2}x+1) using your preferred method.

Also, you may prefer to post such questions in the Maths forum.
(edited 8 years ago)
to factorise

ax2 + bx + c you multiply a & c

then look for factor pairs of ac which can make b... let us suppose that a suitable pair is d & e

so you can rewrite bx as dx + ex...

==== > ax2 + dx + ex + c

now factorise the first two terms... ax2 + dx

to get

fx( gx + h )

then find i such that

i( gx + h ) is the same as ex + c

finally write out the double brackets:

(fx + i) ( gx + h )


:hat2:
Reply 3
Avatar for AxSirlotl
AxSirlotl
OP
18
Thanks! When I try to post in the maths forum it keeps saying "something went wrong, try again" :/
Reply 4
Avatar for joostan
joostan
13
Original post by AxSirlotl
Thanks! When I try to post in the maths forum it keeps saying "something went wrong, try again" :/


You're welcome, and how bizarre. :redface:
Reply 5
Avatar for Zacken
Zacken
22
Original post by AxSirlotl
Thanks! When I try to post in the maths forum it keeps saying "something went wrong, try again" :/


Go directly to the maths forum and click the "compose new thread" button, don't use the TSR tool for selecting which forum you want your question posted in or whatever, it's messed up.

I've moved this to the maths forum, for now.
Reply 6
Avatar for AxSirlotl
AxSirlotl
OP
18
Original post by Zacken
Go directly to the maths forum and click the "compose new thread" button, don't use the TSR tool for selecting which forum you want your question posted in or whatever, it's messed up.

I've moved this to the maths forum, for now.


Thanks :3
The 'ac' method is normally quite good if you just can't see the factorised version straight away:
2x^2 + 5x + 2
multiply a and c together:
2 * 2 = 4
find two numbers that multiply to make 4 and add to make 5:
1 and 4
re-write the equation using these two numbers as the middle terms:
2x^2 + x + 4x + 2
factorise each 'half':
x(2x + 1) + 2(2x+ 1)
here you can see that '2x + 1' is multiplied by both x and 2, so you can write this using brackets:
(2x + 1)(x+2)

boom, factorised :biggrin: @AxSirlotl

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