what is the answer to 2x^2+3x+6

Question

Factoring polynomials if possible

Answer 1

2x²+3x+6 has only complex zeroes.

This can be written:

2(x²+3x/2+3)=

2(x²+3x/2+9/16-9/16+3)=

2((x+¾)²+39/16)=2((x+¾)²-(-√39/4)²).

This is now presented fundamentally as difference of two squares, which can be factorised:

2(x+¾-√(-39)/4)(x+¾+√(-39)/4). Since there is no real square root of a negative number, this can't be factorised into real factors.