Solving quadratic equations by factoring

Solving quadratic equations by factoring

Review the chapter on "Factoring" to refresh your memory if you don't quite remember how to factor polynomials. It will definitely help you solve the questions in this lesson!
Basic concepts: Factoring polynomials: ax2+bx+cax^2 + bx + c, Factoring perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2, Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2), Solving polynomial equations,
Related concepts: System of linear-quadratic equations, System of quadratic-quadratic equations, Graphing quadratic inequalities in two variables,

Lessons

Difference of Squares: a2−b2=(a+b)(a−b)a^2-b^2=(a+b)(a-b)
  • Introduction
    a)
    Solve by factoring a trinomial: 2x2−12x+10=02x^2-12x+10=0

    b)
    Solve by factoring a difference of squares: 25x2−49=025x^2-49=0

  • 1.
    Solve by Factoring a Trinomial
    Solve each equation by factoring.
    a)
    3x2+x−10=03x^2+x-10=0

    b)
    7x2+35=−42x7x^2+35=-42x

  • 2.
    Solve by Factoring a Difference of Squares
    Solve each equation by factoring.
    a)
    x2−36=0 x^2-36=0

    b)
    36x2−25=0 36x^2-25=0

    c)
    12x3−75x=0 12x^3-75x=0

    d)
    40−10x2=0 40-10x^2=0

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20.
Solving Quadratic Equations
20.1
Solving quadratic equations by factorising
20.2
Solving quadratic equations by completing the square
20.3
Using quadratic formula to solve quadratic equations
20.4
Nature of roots of quadratic equations: The discriminant
20.5
Applications of quadratic equations
GCSE Maths
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