To determine the factors of the quadratic polynomial [tex]\( m^2 - 14m + 48 \)[/tex], follow these steps:
1. Identify Coefficients: Examine the polynomial [tex]\( m^2 - 14m + 48 \)[/tex].
- The coefficient of [tex]\( m^2 \)[/tex] is 1.
- The coefficient of [tex]\( m \)[/tex] is -14.
- The constant term is 48.
2. Factorization Method: For a quadratic polynomial of the form [tex]\( m^2 + bm + c \)[/tex], we look for two numbers that multiply to [tex]\( c \)[/tex] (the constant term) and add up to [tex]\( b \)[/tex] (the coefficient of the middle term).
3. Finding Numbers:
- Here, we need two numbers that multiply to 48 and add up to -14.
4. Possible Pairs:
- Consider pairs of factors of 48:
- (1, 48), (2, 24), (3, 16), (4, 12), (6, 8)
- Among these, the pair that adds up to -14 is (6, 8), but since both terms are negative for an addition to yield -14, we use -6 and -8.
5. Verification:
- Check that [tex]\((-6) \times (-8) = 48\)[/tex] and [tex]\((-6) + (-8) = -14\)[/tex].
6. Writing the Factors:
- The factors of the polynomial [tex]\( m^2 - 14m + 48 \)[/tex] are therefore [tex]\((m - 6)\)[/tex] and [tex]\((m - 8)\)[/tex].
Thus, we can rewrite the polynomial as:
[tex]\[
m^2 - 14m + 48 = (m - 6)(m - 8)
\][/tex]
Hence, the best answer is:
D. [tex]\((m - 6)(m - 8)\)[/tex]
