How do you factor # 12x^2+19x+5#?

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Answer 1 · 2015-05-02T07:12:53

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 = 12*5 = 60#
AND
#N_1 +N_2 = b = 19#

After trying out a few numbers we get #N_1 = 15# and #N_2 =4#

#15*4 = 60#, and #15+4= 19#

#12x^2+19x+5 = 12x^2 + 15x +4x + 5#

# = 3x(4x + 5) + 1(4x+5)#

#4x+5# is a common factor to each of the terms

# =color(green)( (4x+5)(3x+1)#