How do you factor the expression #6x^2+14x+4#?

1 Answer
Bill Jorgensen
Jun 21, 2018

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

Explanation:

#6x^2+14x+4#

first factor out the GCF using the distributive property:

#2(3x^2+7x+2)#

Factor by grouping, we need a pair of numbers whose sum is #7# and product is #3*2=6# it is immediately clear that #1# and #6# will work, so replace the #7x# with #6x+1x#

#2(3x^2+7x+2)#

#2(3x^2+6x+x+2)#

now factor:

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

now factor out the #(x+2)#:

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

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