Solving Quadratics by Factorising

Solving Quadratics by Factorising

Solving quadratics by factorising

How do I solve a quadratic equation using factorisation?

• Rearrange it into the form ax² + bx + c = 0

  • zero must be on one side

    • it is easier to use the side where a is positive

• Factorise the quadratic and solve each bracket equal to zero

  • If (x + 4)(x - 1) = 0, then either x + 4 = 0 or x - 1 = 0

    • Because if A × B = 0, then either A = 0 or B = 0

• To solve $\left(x-3\right)\left(x+7\right)=0$

  • …solve “first bracket = 0”:

    • x – 3 = 0 

    • add 3 to both sides: x = 3

  • …and solve “second bracket = 0”

    • x + 7 = 0

    • subtract 7 from both sides: x = -7

  • The two solutions are x = 3 or x = -7

    • The solutions have the opposite signs to the numbers in the brackets

• To solve $\left(2x-3\right)\left(3x+5\right)=0$

  • …solve “first bracket = 0”

    • 2x – 3 = 0

    • add 3 to both sides: 2x = 3

    • divide both sides by 2: x = $\frac{3}{2}$

  • …solve “second bracket = 0”

    • 3x + 5 = 0

    • subtract 5 from both sides: 3x = -5

    • divide both sides by 3: x = $-\frac{5}{3}$

  • The two solutions are x = $\frac{3}{2}$ or x = $-\frac{5}{3}$

• To solve $x\left(x-4\right)=0$

  • it may help to think of x as (x – 0) or (x)

  • …solve “first bracket = 0” 

    • (x) = 0, so x = 0

  • …solve “second bracket = 0”

    • x – 4 = 0

    • add 4 to both sides: x = 4

  • The two solutions are x = 0 or x = 4

    • It is a common mistake to divide both sides by x at the beginning - you will lose a solution (the x = 0 solution)