For some real number $r,$ the polynomial $8x^3 - 4x^2 - 42x + 45$ is divisible by $(x - r)^2.$ Find $r.$

My go at it:

I immediately tried factoring it, and magically, the factored expression was:

$(2x-3)^2(2x+5)$, obviously we want (x-r)^2 to be divisible so I though 3x+3 would divide the $(2x-3)^2$,

however the question is asking for a real number $r$, then is there a number $r3?,

Remember, vietas formula for three roots is for x, y, z are roots,

x+y+z=-b/a

xy+yz+xz=c/a

xyz=-d/a

for a cubic polynomial ax^3+bx^2+cx+d

Guest Jan 1, 2021