To factor the given trinomial [tex]\( m^2 + 12m + 35 \)[/tex], we look for two numbers that multiply to the constant term, 35, and add up to the coefficient of the linear term, 12.
1. Identify the constant term and the coefficient of the linear term:
- Constant term (product): 35
- Coefficient of the linear term (sum): 12
2. Find two numbers that multiply to 35 and add up to 12. These numbers are 5 and 7:
- [tex]\( 5 \times 7 = 35 \)[/tex]
- [tex]\( 5 + 7 = 12 \)[/tex]
3. Use these numbers to factor the trinomial into two binomials:
- [tex]\( m^2 + 12m + 35 = (m + 5)(m + 7) \)[/tex]
Thus, the factors of the trinomial [tex]\( m^2 + 12m + 35 \)[/tex] are [tex]\( (m + 5) \)[/tex] and [tex]\( (m + 7) \)[/tex].
So, the correct answers are:
- The factors of [tex]\( m^2 + 12m + 35 \)[/tex] are [tex]\( (m + 5) \)[/tex] and [tex]\( (m + 7) \)[/tex].
