How do you factor #3x^2 + 5x - 2 = 0#?

1 Answer
Apr 1, 2016

Answer:

# color(blue)( (3x - 1) ( x + 2 ) # is the factorised form of the expression.

Explanation:

#3x^2 + 5x -2 = 0#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 3*(-2) = - 6#

AND

#N_1 +N_2 = b = 5#

After trying out a few numbers we get #N_1 = -1# and #N_2 =6#

#6*(-1) = -6#, and #6+(-1)= 5#

#3x^2 + 5x -2 = 3x^2 + 6x -1x-2#

# = 3x ( x + 2 ) -1 ( x + 2)#

# =color(blue)( (3x - 1) ( x + 2 ) #

# color(blue)( (3x - 1) ( x + 2 ) # is the factorised form of the expression.