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1. Type I-Factorization by common factor

Factorisation by taking out the common factor from each term

1. Consider the expression

3 x^{3} - 15 x^{2} + 12 x

In all the term,

3 x

is taken commonly outside.

(3 x \times x^{2}) + (3 x \times - 5 x) + (3 x \times 4)

= 3 x (x^{2} - 5 x + 4)

2. Consider the expression

10 xy + 5 x^{3} y

Here the term

5 xy

is common in the expression.

10 xy + 5 x^{3} y

\begin{array}{l} = (5 xy \times 2 + 5 xy \times x^{2}) \\ = 5 xy (2 + x^{2}) \end{array}

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