How do you factor #4x^2-38x+18#?

1 Answer
May 5, 2016

Answer:

# (4x - 2 ) ( x - 9)# is the factorised form of the expression.

Explanation:

#4x^2 - 38x + 18#

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 = 4 * 18 = 72#

AND

#N_1 +N_2 = b = -38 #

After trying out a few numbers we get #N_1 = -36 # and #N_2 =-2#
#(-36) *( - 2) = 72#, and # (-36)+(-2)= -38#

#4x^2 - 38x + 18 = 4x^2 - 36x - 2x + 18#

# = 4x ( x - 9) - 2 ( x - 9 )#
# = (4x - 2 ) ( x - 9) #