Question

simon is factoring the polynomial.\\(x^2 - 4x - 12\\)\\((x - 6)(x + \underline{quadquad})\\)\
what value should simon write on the line?\
\\(\circ -6\\)\
\\(\circ -2\\)\
\\(\circ 2\\)\
\\(\circ 6\\)

Explanation:

Step1: Recall factoring quadratic rule

For $x^2+bx+c=(x+m)(x+n)$, $m+n=b$, $m \times n=c$

Step2: Set up equations for unknown

Let unknown = $k$. We know:
$-6 + k = -4$, $-6 \times k = -12$

Step3: Solve for k

From $-6 + k = -4$, calculate $k = -4 + 6 = 2$
Verify: $-6 \times 2 = -12$, matches constant term.

Answer:

C. 2