Question

How to factor 5x^2 +4x -1

Answer 1

`5x^2+4x-1\\\\Method\ 1:\\\\5x^2+4x-1=5x^2+5x-x-1=5x(x+1)-1(x+1)\\=(x+1)(5x-1)\\\\5x^2+4x-1=(x+1)(5x-1)\\\\Method\ 2:\\\\5x^2+4x-1\\a=5;\ b=4;\ c=-1\\\\\Delta=b^2-4ac\\\\\Delta=4^2-4\cdot5\cdot(-1)=16+20=36 \ \textgreater \ 0\\\\x_1=(-b-\sqrt\Delta)/(2a)\ and\ x_2=(-b+\sqrt\Delta)/(2a)\\\\\sqrt\Delta=√(36)=6\\\\x_1=(-4-6)/(2\cdot5)=(-10)/(10)=-1\\\\x_2=(-4+6)/(2\cdot5)=(2)/(10)=0.2\\\\5x^2+4x-1=5(x-0.2)(x+1)=(5x-1)(x+1)`