Answer :
[tex]10x^2+31x+24 = \\ \\=10x^2+31x-15x+15x+24 =\\ \\= 10x^2+16x+15x+24 =\\ \\=2x(5x+8) +3(5x+8)=\\ \\=(5x+8)(2x+3)[/tex]
[tex]10x^2+31x+24\\\\a=10;\ b=31;\ c=24\\\\\Delta=b^2-4ac\\\\\Delta=31^2-4\cdot10\cdot24=961-960=1\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt1=1\\\\x_1=\frac{-31-1}{2\cdot10}=\frac{-32}{20}=-\frac{8}{5};\ x_2=\frac{-31+1}{2\cdot10}=\frac{-30}{20}=-\frac{3}{2}\\\\10x^2+31x+24=10(x+\frac{8}{5})(x+\frac{3}{2})=5(x+\frac{8}{5})\cdot2(x+\frac{3}{2})\\\\=(5x+8)(2x+3)[/tex]
