r is a root of equation x^2 - 3x + 4 = 0. Reduce (r^3 - 4r^2 + 9r - 2) into a linear expression without actually calculating the value of r.

Given that r is a root of equation x^2 - 3x + 4 = 0, which means r should satisfy the equation. So we can say that

(r)^2 - 3(r) + 4 = 0
=> r^2 - 3r + 4 = 0               (1)

Multiplying r on both sides of the equation, we'll get

=> r (r^2 - 3r + 4) = 0 * r
=> r^3 - 3r^2 + 4r = 0          (2)

Now, using (1) and (2), we'll try reducing r^3 - 4r^2 + 9r - 2

=> r^3 - 4r^2 + 9r - 2
=> (r^3 - 3r^2 + 4r) - r^2 + 5r - 2
=> 0 - r^2 + 5r - 2          (by using 2)
=> - (r^2 - 5r + 2)
=> - (r^2 - 3r + 4 - 2r + 2)
=> - (0 - 2r + 2)              (by using 1)
=> 2r - 2
=> 2(r - 1)

which is linear.