How do you solve this problem? x ^(2) - 2x - 3

Question

How do you solve this problem?


`x ^(2) - 2x - 3`

Answer 1

hello :

x² - 2x - 3 = ( x² -2x +1 ) - 2²

= ( x - 1 )² -2²

= ( x - 1 - 2 ) ( x - 1 +2).....by idetity : a² - b² = (a - b) ( a + b )

= ( x - 3 ) ( x + 1)

x² - 2x - 3 = 0 : x - 3 = 0 or x + 1 = 0

so : x = 3 or x = -1

Answer 2

x = - 1, x = 3

Explanation:

Consider the factors of the constant term ( - 3) which sum to give the coefficient of the x- term (- 2)

The factors are - 3 and + 1

(x - 3)(x + 1) ← in factored form

To solve equate to zero, that is

(x - 3)(x + 1) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 1 = 0 ⇒ x = - 1