i'd like some help,could you please help me factorise this expression
$\displaystyle 4x^2+2x-20$
For a polynomial of form $\displaystyle Ax^2+Bx+C$, 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 $\displaystyle 4x^2+2x-20=(2x+5)(2x-4)$
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
For quadratic equations the roots are: $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
now it factorizes to $\displaystyle \left( x-\left(\frac{-b-\sqrt{b^2-4ac}}{2a}\right)\right) \ and\ \left(x-\left(\frac{-b+\sqrt{b^2-4ac}}{2a}\right)\right)$
here $\displaystyle a=4,b=2$ and $\displaystyle c=-20$