← LearnYear 10 Maths · AlgebraFree placement check
Year 10AC9M10A01

Solving Quadratic Equations by Factorising

Expand, factorise and simplify expressions and solve equations algebraically, applying exponent laws involving products, quotients and powers of variables, and the distributive property.

Everything to one side, factorise, then each bracket equals zero.

Worked example

e.g. 2x(x−3)=−3+x(x−10)2x(x-3) = -3 + x(x-10)
  1. Get rid of brackets by multiplying out2x2−6x=−3+x2−10x2x^{2} - 6x = -3 + x^{2} - 10x
  2. Take all terms to the left so the right hand side = 02x2−6x+3−x2+10x=02x^{2} - 6x + 3 - x^{2} + 10x = 0
  3. Simplify terms if possiblex2+4x+3=0x^{2} + 4x + 3 = 0
  4. Factorise the left hand side(x+3)(x+1)=0(x+3)(x+1) = 0
  5. Give the resulting xx value(s)x=−3orx=−1x = -3 \quad \text{or} \quad x = -1

Practice

1
x2+5x+6=0x^{2} + 5x + 6 = 0
Answerx=−2 or x=−3x = -2 \text{ or } x = -3
2
x2−7x+12=0x^{2} - 7x + 12 = 0
Answerx=3 or x=4x = 3 \text{ or } x = 4
3
x2−16=0x^{2} - 16 = 0
Answerx=4 or x=−4x = 4 \text{ or } x = -4
4
2x2+7x+3=02x^{2} + 7x + 3 = 0
Answerx=−3 or x=−12x = -3 \text{ or } x = -\tfrac{1}{2}
5
x(x−5)=6x(x-5) = 6
Answerx=6 or x=−1x = 6 \text{ or } x = -1
6
3x2=12x3x^{2} = 12x
Answerx=0 or x=4x = 0 \text{ or } x = 4
Next step
Practise Solving Quadratic Equations by Factorising with instant marking
A free 10-minute placement check finds which Year 10 topics to work on first, then Summit builds a weekly plan around them.
See where my child is →