Question

I need help factoring  quadratic equation

10x^2+31x+24

Answer 1

`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=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\\\\\sqrt\Delta=\sqrt1=1\\\\x_1=(-31-1)/(2\cdot10)=(-32)/(20)=-(8)/(5);\ x_2=(-31+1)/(2\cdot10)=(-30)/(20)=-(3)/(2)\\\\10x^2+31x+24=10(x+(8)/(5))(x+(3)/(2))=5(x+(8)/(5))\cdot2(x+(3)/(2))\\\\=(5x+8)(2x+3)`

Answer 2

`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)`