To factor the trinomial [tex]\( m^2 + 12m + 35 \)[/tex], we need to find two numbers that multiply to 35 and add up to 12.
Here’s the detailed step-by-step solution:
1. Identify the trinomial: We start with the trinomial [tex]\( m^2 + 12m + 35 \)[/tex].
2. Find two numbers whose product is 35 and whose sum is 12:
- We look for pairs of factors of 35: [tex]\( 1 \cdot 35 \)[/tex], [tex]\( 5 \cdot 7 \)[/tex].
- Out of these pairs, the pair that sums to 12 is [tex]\( 5 \)[/tex] and [tex]\( 7 \)[/tex] since [tex]\( 5 + 7 = 12 \)[/tex].
3. Write the trinomial in factored form:
- Using the numbers 5 and 7, we can write the trinomial as a product of two binomials:
- The trinomial [tex]\( m^2 + 12m + 35 \)[/tex] factors into [tex]\( (m + 5)(m + 7) \)[/tex].
Thus, the factors of [tex]\( m^2 + 12m + 35 \)[/tex] are [tex]\( \boxed{m+5} \)[/tex] and [tex]\( \boxed{m+7} \)[/tex].
The correct answers for the drop-down menus are:
- The first box should have [tex]\( m + 5 \)[/tex].
- The second box should have [tex]\( m + 7 \)[/tex].
