1. factorise

can $3x^2+2x-5$ be factorised?

2. Originally Posted by decoy808
can $3x^2+2x-5$ be factorised?
is $b^2-4ac$ a perfect square number?

if yes, then the quadratic is factorable.

if not, then no.

3. $(x-1)(3x+5)$

4. Originally Posted by Raoh
$(x-1)(3x+5)$
Because $b^2-4ac$ is a perfect square.( $\Delta =64$ )
if $b^2-4ac$ was negative or not a perfect square we wouldn't be able to factorize.(as Skeeter said )

5. Originally Posted by decoy808
can $3x^2+2x-5$ be factorised?
split coefficient of $x^2$, ie. 3, into its factors 3x and 1x. also split the constant -5 into -1 and +5
you will find that:
3 x -1 = -3
1 x +5 = +5
putting these two products together you have (-3) + (+5) = (+2), which is the coefficient of x. however when you fill up the brackets with these factors you don't write (3x - 1)(x + 5). You write (3x + 5)(x - 1).