Question

what is the factored form of ( x^2 - 4x - 5 )?
( (x + 5)(x - 1) )
( (x + 5)(x + 1) )
( (x - 5)(x - 1) )
( (x - 5)(x + 1) )

Explanation:

Step1: Recall factoring quadratic

We need to factor \(x^2 - 4x - 5\). For a quadratic \(ax^2+bx+c\) (here \(a = 1\), \(b=-4\), \(c = - 5\)), we find two numbers that multiply to \(ac=1\times(-5)=-5\) and add to \(b=-4\). The numbers are \(-5\) and \(1\) since \(-5\times1=-5\) and \(-5 + 1=-4\).

Step2: Rewrite and factor

Rewrite the middle term: \(x^2-5x + x-5\). Group the terms: \((x^2 - 5x)+(x - 5)=x(x - 5)+1(x - 5)=(x - 5)(x + 1)\).

Answer:

\((x - 5)(x + 1)\) (the fourth option)