๐ Topic Summary
Factoring quadratic expressions 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 quadratic expression in factored form as $(x + p)(x + q)$, where $p$ and $q$ are the two numbers. This printable activity will guide you through the process with clear explanations and exercises.
For example, to factor $x^2 + 5x + 6$, we need to find two numbers that add to 5 and multiply to 6. These numbers are 2 and 3. Therefore, the factored form is $(x + 2)(x + 3)$.
๐ง Part A: Vocabulary
- ๐งฎ Term 1: Quadratic Expression
- ๐ Definition 1: An expression of the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.
- ๐งฎ Term 2: Factor
- ๐ Definition 2: To express a number or algebraic expression as a product of two or more factors.
- ๐งฎ Term 3: Constant
- ๐ Definition 3: A fixed value that does not change.
- ๐งฎ Term 4: Coefficient
- ๐ Definition 4: A number multiplied by a variable in an algebraic expression.
- ๐งฎ Term 5: FOIL Method
- ๐ Definition 5: A technique used to multiply two binomials: First, Outer, Inner, Last.
๐ Part B: Fill in the Blanks
To factor the quadratic expression $x^2 + bx + c$, we need to find two numbers that ______ to $b$ and ______ to $c$. These numbers are then used to rewrite the quadratic expression in ______ form. For example, to factor $x^2 + 7x + 12$, we need to find two numbers that add to ______ and multiply to ______. These numbers are 3 and ______. Therefore, the factored form is $(x + 3)(x + 4)$.
๐ก Part C: Critical Thinking
Explain in your own words why understanding factoring is important in solving quadratic equations and simplifying algebraic expressions. Give an example of a real-world situation where factoring might be useful.