Question

I will rate brainliest to the fastest and correct answer: Find the constant c such that (x^2-4x+3)(x+5) - (x^2+4x-5)(x-c)=0 for all x.

Answer 1

The problem means that both polynomials have to be the same:

(x^2-4x+3)*(x+5) = (x^2+4x-5)*(x-c)

But they look different. So one has to find all the roots.

x^2-4x+3 = (x-1)(x-3)
x^2+4x-5 = (x-1)(x+5)

So, the problem is indeed find 'c' such that the equality always holds:

(x-1)(x-3)(x+5) = (x-1)(x+5)(x-c),

And, therefore, c=3.

Hope it may still help.