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Manipulating and factorising polynomialsEdexcel International A Level Maths: Flashcards

What these 13 flashcards ask

  • What is the degree of a polynomial?
  • What does f(a) mean?
  • What is the first step when factorising?
  • Fully factorise x^3+4x^2+3x.
  • Factorise x^2-9.
  • State the difference of two squares.
  • Expand (x+3)^2.
  • Expand (x-2)^3.
  • What are like terms?
  • Factorise 2x^3-8x^2+6x.
  • For x^2+bx+c factorising as (x+p)(x+q), what must p and q satisfy?
  • Why can x^2+9 not be factorised over the reals?
  • If f(x)=x^2-3x+1, find f(-2).

Exam questions on Manipulating and factorising polynomials

  1. The polynomial f(x)=x3+4x2+3xf(x)=x^3+4x^2+3x is defined for real xx.
    Solve f(x)=0f(x)=0.2 marks
  2. The function g(x)=(2x−1)(x+3)2g(x)=(2x-1)(x+3)^2 is defined for real xx.
    Show that g(x)=2x3+11x2+12x−9g(x)=2x^3+11x^2+12x-9.2 marks
  3. The polynomials h(x)=x3−9xh(x)=x^3-9x and k(x)=x2−x−12k(x)=x^2-x-12 are defined for real xx.
    Factorise h(x)h(x) completely.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).