Question

Factorise x³+3x²+5x+6​

Answer 1

Answer:

Given:-

${x}^{3} + 3 {x}^{2} + 5x + 6$

By hit and trial I found x+2 as it's factor

x+2=0

x= -2

Substituting x:

${ - 2}^{3} + 3 \times { - 2}^{2} + 5 \times - 2 + 6 = 0$

= -8+3×4-10+6=0

= -8+12-10+6=0

= -18+18=0

0=0

Hence it is found that x+2 is it's factor

Now factorising it:-

See in the attachment

Final answer:-

$(x + 2)( {x}^{2} + x + 3)$