### Theory:

**Factorisation**:

It is the reverse process of multiplication.

Example:

The factors \(x+1\) and \(x+2\) are multiplied as follows to get a quadratic polynomial.

\(x+1\) \(\cdot\) \(x+2\) \(=\) \(x^2 + x + 2x + 2\)

\(=\) \(x^2 + 3x + 2\)

\(x^2 + 3x + 2\) is factorised to get the factors \(x+1\) and \(x+2\).

**:**

*Ways of factorisation*There are two ways of factorization

- By factoring out the common term.

Example:

Factorise \(ax^2 + bx\).

**Solution**:

Here \(x\) is the common term in the polynomial \(ax^2 + bx\).

Factor out \(x\) from the polynomial \(ax^2 + bx\).

\(ax^2 + bx\) \(=\) \(x(ax + b)\)

The factors of \(ax^2 + bx\) are \(x\) and \(ax + b\).

- By grouping the items in an expression.

Example:

Factorise \(ax + a + bx + b\).

**Solution**:

Group the identical terms in the polynomial \(ax + c + bx + b\).

\(ax + a + bx + b\) \(=\) \((ax + a) + (bx + b)\)

\(=\) \(a(x + 1) + b(x + 1)\)

Factor out the common terms in the above expression.

\(ax + a + bx + b\) \(=\) \((x + 1)(a + b)\)

The factors of \(ax + a + bx + b\) are \((x + 1)\) and \((a + b)\).