# Thread: factorise help

1. ## factorise help

i'd like some help,could you please help me factorise this expression

$4x^2+2x-20$

2. Originally Posted by johnsy123
i'd like some help,could you please help me factorise this expression

$4x^2+2x-20$
For a polynomial of form $Ax^2+Bx+C$, factoring is always tougher when A is greater than 1, so this involves some guess and check and as you become more familiar you can quickly do this

For instance I can see that $4x^2+2x-20=(2x+5)(2x-4)$

Now how I got that?

A=4 in this case, so the options for the first numbers in the parenthesis are (2x )(2x ) or (4x )(x ) since 4's factors are 1,2,2,4

Then 20, which has factors 1,2,4,5,10,20

We need the factors to multiply to -20 though, so one of the numbers in the parenthesis must be negative

so we can try (2x- )(2x+ ) or (4x- )(x+ ) or (4x+ )(x- )

now it's just a matter of how quickly you can choose factors and multiply in your head (or on paper), if we try 1 and 20 in (2x- )(2x+ ), you can see there is no way to add to +2, same with 2 and 10, but 4 and 5 do work

if the 5 is positive and the 4 is negative, 5*-4=-20 and 2x*5+2x*-4=+2x

so our answer is (2x-4)(2x+5)

luckily we tried this before going onto the possibilities of (4x- )(x+ ) or (4x+ )(x- ), that can happen though and these problems could take a few minutes to solve

there are other ways of factoring, but I find this way quickest and most effective with enough practice

3. $4x^2+2x-20$
Actually, the first thing you should do first is to factor out any GCFs (greatest common factors):
$2(2x^2+x-10)$
and then go through the steps that artvandalay11 wrote above:
$2(2x + 5)(x - 2)$

01

4. Originally Posted by johnsy123
i'd like some help,could you please help me factorise this expression

$4x^2+2x-20$
For quadratic equations the roots are: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

now it factorizes to $\left( x-\left(\frac{-b-\sqrt{b^2-4ac}}{2a}\right)\right) \ and\ \left(x-\left(\frac{-b+\sqrt{b^2-4ac}}{2a}\right)\right)$

here $a=4,b=2$ and $c=-20$