Question

It says write the function as a product of linear and irreducible quadratic factors all with real coefficients, the problem is: f(x)= 3x^3 - 2x^2 + x - 2

Answer 1

We start by guessing possible roots to the equation f(x) = 0.
If x = 1, then f(1) = 3 - 2 + 1 - 2 = 0, so 1 is a root, and (x - 1) is a factor (our linear factor).
If we divide f(x) by (x - 1) we get (3x^2 + x + 2), which is our quadratic factor.
\[f(x) = 3x^3 - 2x^2 + x - 2 = (x - 1)(x^3 + x + 2)\]

Answer 2

thank you so much