How do I solve a cubic?

You can solve a cubic by applying factor theorem. This is where you plug different values for x into your cubic f(x) = ax^3 + bx^2 + cx + d such that x is a factor of d, until you find a value t for which f(t) = 0. From here factorise the cubic and solve the remaining quadratic equation by the same method, by factorisation, completing the square or by the quadratic formula.

HW

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a typical question would be a setof parametric equations y(t) and x(t), asking you to find dy/dx and then the tangent/normal to the curve at a certain point (ie t = 2)