Question

Find all real number solutions for:
x^3-5x^2+8x-4

Answer 1

First use the rational root test. Namely, find all possible combinations of q/p where q is the factors of the constant and p is the factors of the leading coefficient.

You will end up with

±1/1, ±2/1, ±2/1, ±4/1

Plugging each of these values into the polynomial you will find that 1/1 is rational zero of the function.

Then you can use the factor theorem and divide the polynomial by qx-p and solve for the rest of the zeros.

So you will get,

\[x^3-5x^2+8x-4/(x-1) = x^2 -4x +4\]

You can get this result by synthetic division or long division

Factoring this result you get x^2 -4x +4 = (x-2)^2

So, in all you get

\[x^3-5x^2+8x-4 =(x-1)(x-2)^2\]

Hope this helps :)

Answer 2

thank you