📚 Topic Summary
Factoring trinomials of the form $x^2 + bx + c$ involves finding two numbers that add up to $b$ and multiply to $c$. These two numbers are then used to rewrite the trinomial as a product of two binomials. For example, to factor $x^2 + 5x + 6$, we need two numbers that add up to 5 and multiply to 6. These numbers are 2 and 3, so the factored form is $(x + 2)(x + 3)$.
This worksheet will help you practice identifying those numbers and writing the factored form correctly. Good luck!
🧠 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Trinomial |
A. A number multiplied by a variable |
| 2. Factor |
B. An expression with three terms |
| 3. Binomial |
C. A number or expression that divides evenly into another number or expression |
| 4. Coefficient |
D. An expression with two terms |
| 5. Constant |
E. A term without a variable |
(Answers: 1-B, 2-C, 3-D, 4-A, 5-E)
✍️ Part B: Fill in the Blanks
When factoring a trinomial in the form $x^2 + bx + c$, we look for two numbers that _____ to $c$ and _____ to $b$. These two numbers will be the _____ terms in our two binomial factors. For example, in $x^2 + 7x + 12$, we need two numbers that multiply to _____ and add to _____. These numbers are 3 and 4, so the factored form is $(x + 3)(x + 4)$.
(Answers: multiply, add, constant, 12, 7)
🤔 Part C: Critical Thinking
Explain in your own words why it is helpful to know the factors of $c$ when factoring the trinomial $x^2 + bx + c$.