Question

Factor completely 4x2 + 25x + 6.

Answer 1

`4x^2+25x+6=0\\\\Method\ 1:\\\\4x^2+25x+6=0\\4x^2+x+24x+6=0\\x(4x+1)+6(4x+1)=0\\(4x+1)(x+6)=0\iff4x+1=0\ or\ x+6=0\\\\4x+1=0\ \ \ |subtract\ 1\ from\ both\ sides\\4x=-1\ \ \ \ |divide\ both\ sides\ by\ 4\\\boxed{x=-(1)/(4)}\\\\x+6=0\ \ \ \ |subtract\ 6\ from\ both\ sides\\\boxed{x=-6}\\\\therefore\\\\4x^2+25x+6=4\left(x+(1)/(4)\right)(x+6)`



`Method\ 2:\\\\4x^2+25x+6=0\\a=4;\ b=25;\ c=6\\\\\Delta=b^2-4ac\\\\\Delta=25^2-4\cdot4\cdot6=625-96=529 \ \textgreater \ 0\\\\x_1=(-b-\sqrt\Delta)/(2a)\ and\ x_2=(-b+\sqrt\Delta)/(2a)\\\\\sqrt\Delta=√(529)=23\\\\x_1=(-25-23)/(2\cdot4)=(-48)/(8)=-6\\\\x_2=(-25+23)/(2\cdot8)=(-2)/(8)=-(1)/(4)\\\\therefore\\\\4x^2+25x+6=4(x+6)\left(x+(1)/(4)\right)`