### 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 $$(a + b)$$.