Question

How do I work out A & B ?

Answer 1

a)

`(x + 2)(x + 3)`

b)

`x = 2 \: or \: x = 3`

Explanation:

a)
`{x}^(2) + 5x + 6`

`= {x}^(2) + 2x + 3x + 6`

`= x(x + 2) + 3(x + 2)`

`= (x + 2)(x + 3)`

b)

`{x}^(2) + 5x + 6 = 0`

`{x}^(2) + 2x + 3x + 6 = 0`

`x(x + 2) + 3(x + 2) = 0`

`(x + 2)(x + 3) = 0`

`so \: either \: x + 2 = 0 \: or \: x + 3 = 0`

`therefore \: x = - 2 \: or \: x = - 3`

Answer 2

see explanation

Explanation:

(a)

Given

x² + 5x + 6

Consider the factors of the constant term ( + 6) which sum to give the coefficient of the x- term ( + 5)

The factors are 3 and 2, since

3 × 2 = 6 and 3 + 2 = 5, hence

x² + 5x + 6 = (x + 3)(x + 2) ← in factored form

(b)

To solve

x² + 5x + 6 = 0 ← use the factored form, that is

(x + 3)(x + 2) = 0

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x + 2 = 0 ⇒ x = - 2