Prove (a-x)is a factor of (x-a)^3+(x-b)^3+(x-c)^3=0
Im not too sure what to do, would appreciate help
2 answers
Long divide or use synthetic division : )
(x-a)^3 = -(a-x)^3
So that means we have
(a-x)^3 = (x-b)^3 + (x-c)^3
now, using the sum of cubes formula,
(a-x)^3 = (x-b+x-c)((x-b)^2 - (a-b)(x-c) + (x-c)^2)
since the right side is the product of two factors,
(a-x) must divide one of them.
So that means we have
(a-x)^3 = (x-b)^3 + (x-c)^3
now, using the sum of cubes formula,
(a-x)^3 = (x-b+x-c)((x-b)^2 - (a-b)(x-c) + (x-c)^2)
since the right side is the product of two factors,
(a-x) must divide one of them.
0 answers