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Write the equation of a rational function with the following characteristics: Vertical asymptotes at x =...

Write the equation of a rational function with the following characteristics: Vertical asymptotes at x = 3 and x = -4, a horizontal asymptote at y = 0, no x-intercepts and a y-intercept at (0, 1/6).

Consider the polynomial q(x) = 3x2 - 11x2 + kx + 8. Given that q(x) has a factor (x - 4), find the value of k:

Hence or otherwise, factorize q(x) as a product of linear factors.

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