Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients.(a)    x − 30x2 + x − 30

I'm sorry, but the function you provided seems to be incorrect. It's not a rational function (a ratio of two polynomials) which is necessary for a partial fraction decomposition.

A correct rational function should look something like this: (2x^2 + 3x + 1) / (x^2 - x - 6)

Please provide a correct rational function for the partial fraction decomposition.

I'm sorry, but there seems to be a mistake in your question. The function you provided, x - 30x^2 + x - 30, simplifies to -30x^2 + 2x - 30. This is a quadratic function, not a rational function, so it cannot be decomposed into partial fractions.

Partial fraction decomposition is used for rational functions, where the degree of the numerator is less than the degree of the denominator. If you have a rational function that you'd like to decompose into partial fractions, please provide it and I'd be happy to help.