Question

how to factorise 24x^2+9x+5

Answer 1

Equation at the end of step  1  :

((23•3x2) + 9x) + 5

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  24x2+9x+5 

The first term is,  24x2  its coefficient is  24 .
The middle term is,  +9x  its coefficient is  9 .
The last term, "the constant", is  +5 

Step-1 : Multiply the coefficient of the first term by the constant   24 • 5 = 120 

Step-2 : Find two factors of  120  whose sum equals the coefficient of the middle term, which is   9 .

     -120   +   -1   =   -121     -60   +   -2   =   -62     -40   +   -3   =   -43     -30   +   -4   =   -34     -24   +   -5   =   -29     -20   +   -6   =   -26


For tidiness, printing of 26 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !! 
Conclusion : Trinomial can not be factored

Final result :

24x2 + 9x + 5