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Polynomials, factor theorem and algebraic divisionEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

  • State the factor theorem.
  • Which value of x do you test for the factor (x+3)?
  • Which value of x do you test for the factor (2x-1)?
  • What does a zero remainder tell you?
  • Divide x^2+5x+6 by (x+2).
  • Fully factorise x^3+3x^2-4.
  • Fully factorise 6x^3+11x^2-x-6.
  • What is a repeated root?
  • Quotient of (2x^3+x^2-13x+6)\div(x-2)?
  • Three steps to factorise a cubic?
  • How do you find an unknown constant given a factor (x-k)?
  • What do you do about a missing power when dividing?

Exam questions on Polynomials, factor theorem and algebraic division

  1. The polynomial f(x)=x3+3x2−4f(x)=x^3+3x^2-4.
    Hence solve f(x)=0f(x)=0, stating which root is repeated.2 marks
  2. The polynomial g(x)=2x3+x2−13x+6g(x)=2x^3+x^2-13x+6.
    Given that (x−2)(x-2) is a factor, factorise g(x)g(x) completely.2 marks
  3. The polynomial p(x)=2x3+ax2−x+6p(x)=2x^3+ax^2-x+6, where aa is a constant, has a factor (x−2)(x-2).
    Find the value of aa.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).