Factor 4n^2 -4n+3

Question

Factor it

Answer 1

4n²-4n-3=(2n-3)(2n+1).

But 4n²-4n+3 factorises into complex factors only so there are no real solutions.

In case you were expecting complex factors, here is the solution:

4n²-4n+3=4(n²-n+¾)=

4(n²-n+¼-¼+¾)=

4((n-½)²+½)=

4(n-½+i/√2)(n-½-i/√2), where i=√-1.

This can be written:

(2n-1+i√2)(2n-1-i√2).