Question

#8 $x^2 + 13x + 12$
a.
$a = 1$
$b = 13$
$c = 12$
$(x )(c )$

Explanation:

Step1: Identify \(a\), \(b\), \(c\)

For quadratic \(x^2 + 13x + 12\), \(a = 1\), \(b = 13\), \(c = 12\). We need two numbers that multiply to \(a\times c=1\times12 = 12\) and add to \(b = 13\).

Step2: Find the numbers

The numbers are \(1\) and \(12\) (since \(1\times12 = 12\) and \(1 + 12 = 13\)).

Step3: Factor the quadratic

Rewrite the middle term: \(x^2 + x + 12x + 12\). Group and factor: \(x(x + 1)+12(x + 1)=(x + 1)(x + 12)\).

Answer:

\((x + 1)(x + 12)\)