Factorising quadratics
Educational level: this is a secondary education resource. |
Quadratic equations are equations of the form where a, b and c are constants, and is a variable. In other words, a quadratic equation has at least one term of the variable, say , raised to the exponent , e.g.
Subject classification: this is a mathematics resource. |
Arranging termsEdit
Arrange the quadratic into order: first the squared number ax^{2}, then the number times x, bx, finally the constant value c.
Factorising quadraticsEdit
Form of quadratics:
To factorise:
- split the middle term so it adds to the original number, e.g., let b = (AD + BC), and
- multiplies to the constant times the first term, e.g., Ax times Bx equals ABx^{2}, then a = AB,
- then bracket so the pronumeral (letter) is like this, e.g., (Ax + C)(Bx + D).
CheckingEdit
Multiplying the two terms: and with each other becomes:
which rearranges to:
The final constant
ExamplesEdit
To check it, re-expand the answer to see if we get back to where we started from: