How do you factor the expression #2x^2 + 3x + 1#?

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Answer 1 · 2016-03-16T15:56:10

#" "(x+1)(2x+1)#

The only whole number factors of 2 is #1 xx 2#
The only whole number factors of 1 is #1xx1#

The constant of 1 in #2x^2+3x+1# is positive

So the signs in the brackets are the same

#3x# is positive which means, that as the signs are both the same, they have to be positive.

Thus our structure is: #(?+?)(?+?)#

Let us insert the factors. By what was stated earlier we can only have: #(1x+1)(2x+1)#

But it is considered bad practice to write #1x# so we write our factorisation as:

#" "(x+1)(2x+1)#