To factor the trinomial $ b^2 + 8b + 7 $, we need to find two numbers that multiply to give the last number (7) and add up to give the middle coefficient (8).
1.
Identify the numbers:
* We are looking for factors of 7. Since 7 is a prime number, its only whole number factors are 1 and 7.
* Check if they add up to 8: $ 1 + 7 = 8 $. This matches the middle term.
2.
Write the binomials:
* Because the first term is just $ b^2 $, our factored form will start with $(b \dots)(b \dots)$.
* We place our two numbers, 1 and 7, into the empty spots. Since both the addition ($1+7=8$) and multiplication ($1 \times 7 = 7$) result in positive numbers, both signs inside the parentheses will be positive.
* This gives us $(b + 1)$ and $(b + 7)$.
3.
Final Result:
The expression factors completely into $(b + 1)(b + 7)$.
Final Answer: (b + 1)(b + 7)
Parent Tip: Review the logic above to help your child master the concept of factoring worksheet kuta.
