Expressions and equations
An expression, such as \(x^2+x-20\), has a value for each choice of \(x\). An equation, such as \(x^2+x-20=0\), asks which values of \(x\) make the statement true. These values are its solutions or roots.
The zero-product principle
If a product equals zero, at least one factor equals zero: \(AB=0\) means \(A=0\) or \(B=0\). First rearrange the equation so that one side is zero; then factorise.
\(\begin{aligned} (x-4)(x+5)&=0 \\ x-4&=0\quad\text{or}\quad x+5=0 \\ x&=4\quad\text{or}\quad x=-5 \end{aligned}\)
Choosing a method
| What you notice | Useful first step |
|---|---|
| An obvious common factor or factor pair | Factorise after making one side zero. |
| A monic quadratic, \(x^2+bx+c\), or a completing-square instruction | Complete the square. |
| No convenient factorisation | Use the quadratic formula. |
Dividing by an expression containing \(x\) can remove a valid solution when that expression is zero. Factorising keeps that case visible.
Check each proposed solution in the original equation. A correct factorisation is not yet a complete solution until all roots have been stated.
Please join our E Math programme to search for similar questions for more practice.
E Math TuitionNeed help? Join our JC Math tuition classes.
Learn more