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Solving Quadratic Equations by Factorising

Learn how to solve quadratic equations by factorising, like x2+5x+6=0x^2 + 5x + 6 = 0, by writing them as (x+2)(x+3)=0(x+2)(x+3)=0. Let's get started! 🚀

Solving Quadratic Equations by Factorising - introduction visual

Video Lesson

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Flashcards

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Solving quadratic equations by factorisation step-by-step, note finding two numbers that multiply to the constant and add up to the coefficient of x.Solving quadratic equations by factorisation, with example x² + 7x + 12 = 0, note steps to find factors 3 and 4, with solutions.Solving quadratic equations by factorisation: find two numbers that multiply to be the constant (-18) and add up to be the coefficient of x (3).

🛎️ Preparing the Equation

  • Make sure the equation is written as x2+bx+c=0x^2 + bx + c = 0
  • Rearrange first if needed so the equation is equal to zero

🛎️ Factorising the Quadratic

  • Find two numbers mm and nn that multiply to cc and add to bb
  • Write the equation as (x+m)(x+n)=0(x + m)(x + n) = 0
  • Example: (x+3)(x+4)=0(x + 3)(x + 4) = 0

🛎️ Finding the Solutions

  • Set each bracket equal to zero: (x−3)=0(x - 3) = 0 or (x+6)=0(x + 6) = 0
  • Solve to find both values of xx: x=3x = 3 and x=−6x = -6

Practice Questions

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Interactive Activity

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