Question

How to factor completely:  15x²-40x-15

Answer 1

`15x^2-40x-15 =0\ \ /:5\\ \\3x^2-8x-3 =0 \\ \\a=3, \ b=-8 , \ c= -3 \\ \\\Delta =b^2-4ac =(-8)^2 -4\cdot 3\cdot (-3)=64+36=100 \\ \\x_(1)=(-b-\Delta )/(2a)=(8-√(100))/(2 \cdot 3)=(8-10)/(6)=-(2)/(6)=-(1)/(3)`


`x_(2)=(-b+\Delta )/(2a)=(8+√(100))/(2 \cdot 3)=(8+10)/(6)= (18)/(6)=3\\ \\ 3x^2-8x-3 = 3(x+(1)/(3))(x-3)=(3x+1)(x-3) \\ \\ \\Answer : \ 15x^2-40x-15 = 3x^2-8x-3 =(3x+1)(x-3)`