📚 Topic Summary
Factoring a quadratic expression in the form $x^2 + bx + c$ involves finding two numbers that add up to $b$ and multiply to $c$. These numbers are then used to rewrite the quadratic as a product of two binomials. For example, to factor $x^2 + 5x + 6$, we look for two numbers that add to 5 and multiply to 6 (which are 2 and 3). So, $x^2 + 5x + 6 = (x + 2)(x + 3)$. This process simplifies algebraic expressions and helps in solving quadratic equations.
🧮 Part A: Vocabulary
Match the term with its definition:
- Term: Quadratic Expression
- Term: Factor
- Term: Binomial
- Term: Coefficient
- Term: Constant
Definitions:
- A number multiplied by a variable.
- An expression with two terms.
- A value that does not change.
- An expression in the form $ax^2 + bx + c$.
- A number or expression that divides evenly into another number or expression.
(Match the terms above, write your answers on a separate piece of paper!)
✏️ Part B: Fill in the Blanks
To factor $x^2 + bx + c$, we need to find two numbers that __________ to $b$ and __________ to $c$. These two numbers become the __________ terms in our factored expression, which is the product of two __________.
🤔 Part C: Critical Thinking
Explain in your own words why factoring is a useful skill in algebra. Give at least two specific examples of how it can be applied.