How do you factor #8x^2+14x+3#?

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Answer 1 · 2015-10-09T04:41:42

#(4x+1)(2x+3)#

Split 14 in two parts such that sum is 14 and product is 24 as below:

#8x^2 +12x +2x+3#

#(8x^2 +12x) + (2x+3)#

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

#(4x+1)(2x+3)#

Answer 2 · 2015-10-09T04:43:11

# color(blue)( (4x+1)(2x+3) # is the factorised form of the expression.

#8x^2+14x+3#

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*3 = 24#

AND

#N_1 +N_2 = b = 14#

After trying out a few numbers we get #N_1 = 12# and #N_2 =2#
#12*2 = 24#, and #12+2= 14#

#8x^2+color(blue)(14x)+3 =8x^2+color(blue)(12x+2x)+3#

# = 4x(2x+3) +1 (2x+3)#

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

# color(blue)( (4x+1)(2x+3) # is the factorised form of the expression.