How do you factor #14y^2+15y-9#?

1 Answer
Aug 11, 2015

Answer:

# color(blue)(( 7y-3) (2y+3) # is the factorised form of the expression.

Explanation:

#14y^2+15y−9#

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

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

#N_1*N_2 = a*c = 14*-9 = -126#
and,
#N_1 +N_2 = b = 15#

After trying out a few numbers we get #N_1 = 21# and #N_2 =-6#
#21*(-6) = -126#, and #21+(-6)= 15#

#14y^2+color(blue)(15y)−9 = 14y^2+color(blue)(21y -6y)−9#

# = 7y(2y+3) -3 (2y +3)#

# color(blue)(( 7y-3) (2y+3) # is the factorised form of the expression.