To determine the correct factors of the polynomial [tex]\( m^2 - 14m + 48 \)[/tex], we need to factorize the quadratic expression.
Let's break it down step by step:
1. Identify the polynomial to be factored:
[tex]\[ m^2 - 14m + 48 \][/tex]
2. Express the polynomial in the form [tex]\((m - a)(m - b)\)[/tex], where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are two numbers whose product is the constant term (48) and whose sum is the coefficient of the linear term (-14).
3. Find two numbers that multiply to give 48 and add to give -14:
[tex]\[
-6 \times -8 = 48
\][/tex]
and
[tex]\[
-6 + (-8) = -14
\][/tex]
So, the numbers -6 and -8 satisfy both conditions.
4. Write the factors:
Therefore, we can factor the polynomial [tex]\( m^2 - 14m + 48 \)[/tex] as:
[tex]\[
(m - 6)(m - 8)
\][/tex]
Given the choices:
- A. [tex]\((m - 12)(m - 4)\)[/tex]
- B. [tex]\((m - 12)(m + 4)\)[/tex]
- C. [tex]\((m - 6)(m - 8)\)[/tex]
- D. [tex]\((m + 6)(m + 8)\)[/tex]
The correct factorization is given by choice:
- C. [tex]\((m - 6)(m - 8)\)[/tex]
