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Polynomial manipulation and algebraic divisionAQA A-Level Maths: Flashcards

What these 14 flashcards ask

  • What is the degree of a polynomial?
  • Expand (x+2)(x-3)(2x+1).
  • Factorise a^2-b^2.
  • Factorise x^4-81 completely.
  • Factorise 6x^2+7x-3.
  • How do you factorise ax^2+bx+c with a\ne1?
  • What is the first thing to look for when factorising?
  • Factorise x^3+3x^2-4x-12 by grouping.
  • What do you do for a missing power in division?
  • In algebraic division, what is the first step?
  • Divide 3x^3+2x^2-19x+6 by (x-2).
  • How do you write the result of division with a remainder?
  • Divide 2x^3-5x^2+4x-7 by (x-3).
  • How can you check a division?

Exam questions on Polynomial manipulation and algebraic division

  1. Let p(x)=2x3−x2−13x−6p(x)=2x^3-x^2-13x-6 and q(x)=x3+3x2−5x+4q(x)=x^3+3x^2-5x+4.
    Given that (x+2)(x+2) is a factor of p(x)p(x), factorise p(x)p(x) completely.2 marks
  2. The expressions A=x4−81A=x^4-81 and B=6x2+7x−3B=6x^2+7x-3 are to be factorised.
    Factorise completely x3+3x2−4x−12x^3+3x^2-4x-12.2 marks
  3. Let f(x)=3x3+2x2−19x+6f(x)=3x^3+2x^2-19x+6.
    Use algebraic division to show that f(x)=(x−2)(3x2+8x−3)f(x)=(x-2)(3x^2+8x-3).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).