Respuesta :

Answer:

see explanation

Step-by-step 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

colabirb

Answer:

a)

[tex](x + 2)(x + 3)[/tex]

b)

[tex]x = 2 \: or \: x = 3[/tex]

Step-by-step explanation:

a)[tex]{x}^{2} + 5x + 6[/tex]

[tex]= {x}^{2} + 2x + 3x + 6[/tex]

[tex] = x(x + 2) + 3(x + 2)[/tex]

[tex] = (x + 2)(x + 3)[/tex]

b)

[tex]{x}^{2} + 5x + 6 = 0[/tex]

[tex]{x}^{2} + 2x + 3x + 6 = 0[/tex]

[tex]x(x + 2) + 3(x + 2) = 0[/tex]

[tex](x + 2)(x + 3) = 0[/tex]

[tex]so \: either \: x + 2 = 0 \: or \: x + 3 = 0[/tex]

[tex]therefore \: x = - 2 \: or \: x = - 3[/tex]

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