A quadratic expression is an expression with a highest power of x, as 2 or an equation with degreee 2 and the general orm is:

ax^2 + bx+C where a, b and c are numbers.

## Type 1

(For an expression with a coefficient of x equal to 1, (a=1), the given method can be used to factorise)

**Method**

- Find 2 factors of the Constant Term (c), which should add to a coefficient of x
- Write the xpression as a product of two brackets, with a factor in each bracket

**Examples**

- Factorize x
^{2}+ 5x + 6- Factors of 6 that add to 5:
- 2 * 3 = 6
- 2 + 3 = 5

- Answer: (x + 2)(x + 3) OR (x + 3)(x + 2)

- Factors of 6 that add to 5:
- Factorize x
^{2}- 12x + 36- Factors of 36 that add to -12:
- -6 * -6 = 36
- -6 + -6 = -12

- Answer: (x - 6)(x - 6) OR (x - 6)
^{2}

- Factors of 36 that add to -12:
- Factorize x
^{2}+ 8x - 20- Factors of -20 that add to 8:
- 10 * -2 = -20
- 10 + -2 = 10 - 2 = 8

- Answer: (x + 10)(x - 2) OR (x - 2)(x + 10)

- Factors of -20 that add to 8:

## Type 2

(Where the coefficient of x^2 is not a common factor)

**Method**

- Factorise by having the common factor outside the bracket and a quadratic expression inside the bracket
- Furthur factorise the quadratic.

## Type 3

(Where the coefficient of x^2 is not 1 (But not a common factor))

**Method**

- Write ax^2 as two factors and c as two factors.
- Multiply the factors of ax^2 with the factors of the constant term and they should add to bx
- Re-arrange the factors diagonally and write them in two brackets