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Remainder and Factor Theorems — Part 2: Unknown coefficients and factorising cubics completely

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Lesson

Remainder and Factor Theorems, Part 2

A cubic with three zeros splits into three linear factors. The factor theorem finds the first one.

In this lesson you will

  • Find unknown coefficients when one or two factors are given
  • Find a factor of a cubic by trial
  • Divide and factorise a cubic polynomial completely
  • Recognise a quadratic factor that cannot be factorised further, and check a factorisation
  • y=x3+x2−10x+8y = x^3 + x^2 - 10x + 8
Three zeros, three linear factors: $(x + 4)(x - 1)(x - 2)$.