CP1 Roots of Polynomials (Cubics) Fill in the Blanks

This worksheet is designed for Edexcel CP1 Chapter 4, Roots of Polynomials, for students to deduce the patterns in the coefficients of cubic polynomials.
There is a lot of problem solving involved such as forming and solving simultaneous equations, using algebraic division with factor theorem to find a quadratic factor, identifying the complex conjugate as a second root.

When I used this I gave it to the students after we had looked at the patterns in quadratic polynomials and then supported them through questioning but otherwise gave them no further instructions. They then fed back with what their strategy had been, which sections they found most challenging etc.

My class spotted the patterns quickly but found the 5th row a challenge as they didn’t initially consider forming and solving simultaneous equations.