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#1
Hi there, I need to understand how you factorise equations like this.. can someone do the solution so I could follow through thank you
2x^2 + 11x + 12

Thank you
0
1 month ago
#2
=2x^2 8x 3x 12
=2x (x 4) 3(× 4)
=(2x 3)(x 4)
12×2 (1st and last number )=24
24= 2×2×2×3
so u have to make 11 (middle number)
Last edited by Mehz_19; 1 month ago
0
1 month ago
#3
2x^2+8x+3x+12
2x (x+4)+3 (x+4)
(2x+3)(x+4)
0
1 month ago
#4
For my A-Level Maths, I was taught a method for factorising quadratic equations; it'll seem complicated but I'll try to make the method as clear as I can.

So, if the equation is 2x² + 11x + 12...

You'll first want to separate the '11x' part into two additions.
To do this, multiply the 2 (the x² coefficient) with the 12 (the constant, without an x) = 24.
Then, see what two numbers multiply to get 24, while also that add to get 11 (the x coefficient). The two numbers here would be 8 and 3.
Thus, you write the equation as... 2x² + 8x + 3x + 12

With this new equation (where the x coefficient is merely split into two additions), divide it into two halves and factorise so that there is a common factor of each... 2x² + 8x + 3x + 12 will become... 2x(x + 4) + 3(x + 4)

The (x + 4) is the common factor here, so you can write the factorised equation as (2x + 3)(x + 4).

Yeah, I've explained this really badly and I'm certain that somebody will be able to explain this or another method far better - but oh well, it's one way!
1
#5
(Original post by Mehz_19)
=2x^2+8x+3x+12
=2x (x+4)+3(×+4)
=(2x+3)(x+4)
12×2 (1st and last number )=24
24= 2×2×2×3
so u have to make +11 (middle number)
so u have to make
24
(Original post by luke.ah)
For my A-Level Maths, I was taught a method for factorising quadratic equations; it'll seem complicated but I'll try to make the method as clear as I can.

So, if the equation is 2x² + 11x + 12...

You'll first want to separate the '11x' part into two additions.
To do this, multiply the 2 (the x² coefficient) with the 12 (the constant, without an x) = 24.
Then, see what two numbers multiply to get 24, while also that add to get 11 (the x coefficient). The two numbers here would be 8 and 3.
Thus, you write the equation as... 2x² + 8x + 3x + 12

With this new equation (where the x coefficient is merely split into two additions), divide it into two halves and factorise so that there is a common factor of each... 2x² + 8x + 3x + 12 will become... 2x(x + 4) + 3(x + 4)

The (x + 4) is the common factor here, so you can write the factorised equation as (2x + 3)(x + 4).

Yeah, I've explained this really badly and I'm certain that somebody will be able to explain this or another method far better - but oh well, it's one way!
Ahhh thank you! I understood it
3
1 month ago
#6
(Original post by MissCarter786)
Hi there, I need to understand how you factorise equations like this.. can someone do the solution so I could follow through thank you
2x^2 + 11x + 12

Thank you
There is a process called 'completing the square' which will solve any equation like this (or simply use the quadratic formula, although you might not get integer factorisation).

Something you probably learned about half way through the GCSE content.
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