How do you factor #8x^2+18x+9#?

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Answer 1 · 2015-05-02T06:36:42

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 = 8*9 = 72#
AND
#N_1 +N_2 = b = 18#

After trying out a few numbers we get #N_1 = 12# and #N_2 =6#

#12*6 = 72#, and #12+6= 18#

#8x^2+18x+9 = 8x^2 + 12x +6x + 9#

# = 4x(2x + 3) + 3(2x+3)#

#2x+3# is a common factor to each of the terms

# =color(green)( (2x+3)(4x+3)#