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Factorizing expressions
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Factorising simple quadratics
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Factorising complex quadratics

Quadratic factorising

This is one of those iconic maths topics which people talk about, when they want to name-check a difficult pre-16 school level idea. The post-16 equivalent is Calculus.

When you first look at the quadratic expression $x^2+3x+2$, you are likely to think that it cannot be factorised; that it is not the result of a multiplication, but it is fairly straightforward to demonstrate that this is not the case.

$$ \begin{aligned} &\big(x+1 \big)\big(x+2 \big)\\ & = x^2+2x+1x+2 \\ &= x^2+3x+2 \end{aligned} $$

From the calculation above it is clear that $(x+1)$ and $(x+2)$ are both factors of $x^2+3x+2$.

For more details please work through the worked examples on the next tab.