# factorise

• Nov 22nd 2009, 08:44 AM
decoy808
factorise
can \$\displaystyle 3x^2+2x-5\$ be factorised?
• Nov 22nd 2009, 08:51 AM
skeeter
Quote:

Originally Posted by decoy808
can \$\displaystyle 3x^2+2x-5\$ be factorised?

is \$\displaystyle b^2-4ac\$ a perfect square number?

if yes, then the quadratic is factorable.

if not, then no.
• Nov 22nd 2009, 09:01 AM
Raoh
\$\displaystyle (x-1)(3x+5)\$
• Nov 22nd 2009, 09:11 AM
Raoh
Quote:

Originally Posted by Raoh
\$\displaystyle (x-1)(3x+5)\$

Because \$\displaystyle b^2-4ac\$ is a perfect square.( \$\displaystyle \Delta =64\$ )
if \$\displaystyle b^2-4ac\$ was negative or not a perfect square we wouldn't be able to factorize.(as Skeeter said(Happy) )
• Nov 22nd 2009, 09:17 AM
ukorov
Quote:

Originally Posted by decoy808
can \$\displaystyle 3x^2+2x-5\$ be factorised?

split coefficient of \$\displaystyle 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).