How do I decompose this polynomial x^3-5x^2-5x+25?

Answer 1

By decompose do you mean factor?

To factor this polynomial you have to evaluate the (factors of p)/(factors of q) as the first step. p is the constant term, 25 and q is the leading coefficient, 1. The result of this is +/-1, +/-5, +/-25. You can use synthetic division to check each one of these until you find the correct one.

5 works using synthetic division, so this means that 5 is a zero so the first factor is (x-5)

What remains after synthetic division is x^2-5. If you sent this equal to zero and solve, you get the last 2 zeros are +/- radical 5. So the factors are (x+radical 5)(x-radical 5)

The final factored form of this polynomial is: (x-5)(x+radical 5)(x-radical 5)