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The factor theoremAQA A-Level Maths: Flashcards

What these 13 flashcards ask

  • State the factor theorem.
  • Which value do you test to see if (x+3) is a factor?
  • Which value do you test for the factor (2x-3)?
  • Which value do you test for the factor (3x+2)?
  • What does f(a)\ne0 tell you?
  • Which values should you try first when searching for a factor?
  • What are the steps for factorising a cubic?
  • Is (x-1) a factor of 2x^3-x^2-7x+6?
  • How does a factorised polynomial give the solutions of f(x)=0?
  • What does a repeated factor (x-3)^2 mean for f(x)=0?
  • How do you find two unknown coefficients using the factor theorem?
  • (x-2) is a factor of x^3+kx^2-4x+12. Find k.
  • How can you check a factorisation?

Exam questions on The factor theorem

  1. Let f(x)=2x3−x2−7x+6f(x)=2x^3-x^2-7x+6.
    Given that (x−1)(x-1) and (2x−3)(2x-3) are factors of f(x)f(x), factorise f(x)f(x) completely.2 marks
  2. The polynomial p(x)=x3+kx2−4x+12p(x)=x^3+kx^2-4x+12 has (x−2)(x-2) as a factor, where kk is a constant.
    Using your value of kk, solve p(x)=0p(x)=0.2 marks
  3. The cubic g(x)=2x3+ax2+bx−12g(x)=2x^3+ax^2+bx-12, where aa and bb are constants, has factors (x−2)(x-2) and (x+3)(x+3).
    Use the factor theorem to show that 2a+b=−22a+b=-2 and 3a−b=223a-b=22.3 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).