A student said the factors of m^2-10m+24 are (m-12)(m+12). Is the student correct? Justify and explain your answer.
No, the student is not correct. To factor the expression m^2-10m+24, we need to find two numbers that multiply to 24 and add to -10. These numbers are -4 and -6. Therefore, the correct factored form of the expression is (m-4)(m-6), not (m-12)(m+12).
To verify this, we can expand (m-4)(m-6) using the distributive property:
(m-4)(m-6) = m^2 -6m -4m + 24 = m^2 -10m + 24
Thus, the correct factored form of m^2-10m+24 is (m-4)(m-6), not (m-12)(m+12).