Find q(x) and r(x) as described by the division algorithm so that f (x) = g(x)q(x) + r(x) with r(x) = 0 or of degree less than the degree of g(x).

f (x) = x⁶ + 3x⁵ + 4x² - 3x + 2 and g(x) = x² + 2x - 3 in Z₇ [x].