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a. apply the definition of Laplace transform (the integral...). A little tedious but doable. Or, looking in your table, you have tⁿ f(t), which saves you many steps.
b. High School algebra: Rewrite as [steps left for you, partial fractions] 1/(s+3)² - 4/(s+3)³ + 10/(s+3)⁴.
Now, just look in your (inverse) laplace table for each of these. take note of the frequency shift one:
e^(ct)*f(t) becomes F(s-c).
Done!