How do you solve #3x^2 + 9x = 12#?

1 Answer
Apr 4, 2016

Answer:

#" "(3x-3)(x+4)#

With practise these become easier to solve

Explanation:

Given: #" "3x^2+9x=12#

Write as:

#" "3x^2+9x-12=0#

We are looking for #(?x+?)(?x+?)#

The only whole number factors of 12 are
#color(blue)(" "1 ,12)#
#color(blue)(" "2,6)#
#color(blue)(" "3,4)#

This means we can only have one of:
#" "(?x+1)(?x+12)#
#" "(?x+2)(?x+6)#
#" "(?x+3)(?x+4)#

'................................................................

The only whole number factors of 3 are #color(magenta)(1,3)#

So the #?x# can only be these numbers giving:

#" "(color(magenta)(1)x+?)(color(magenta)(3)x+?) -> (x+?)(3x+?)#
'..............................................................

It is now a matter of trying them out and seeing what works.

I spot that from the factors of #color(magenta)(3)# if we have:

#color(magenta)((3color(blue)(xx4))-(1color(blue)(xx3))) #

we have:#" "12-3=9# which will give us #+9x#

So the factorisation must be

#" "(color(magenta)(3x)color(blue)(-3))(color(magenta)(x)color(blue)(+4))#

'~~~~~~~~~~~~~~~~~~~~~
Check

#" "(3x-3)(x+4) #

#" "=" "3x^2+12x-3x-12#
#" "=" "3x^2+9x-12 #