Example Card: Factoring When c is Negative
Factor trinomials where the constant term c is negative by finding factor pairs with opposite signs that sum to the middle coefficient b in Grade 9 Algebra.
Key Concepts
When the last term is negative, things get a little tricky; one factor is positive, and one is negative. This is the other key idea from this lesson.
Factor the trinomial $x^2 + 2x 24$.
1. In this trinomial, $b$ is $2$ and $c$ is $ 24$. 2. We need to find one positive and one negative number that have a product of $ 24$. Let's list the pairs: $$ ( 1)(24) \quad (1)( 24) \quad ( 2)(12) \quad (2)( 12) \quad ( 3)(8) \quad (3)( 8) \quad ( 4)(6) \quad (4)( 6) $$ 3. The sum of only one of these pairs is $2$. $$ ( 1) + 24 = 23 \qquad (1) + ( 24) = 23 $$ $$ ( 2) + 12 = 10 \qquad (2) + ( 12) = 10 $$ $$ ( 3) + 8 = 5 \qquad (3) + ( 8) = 5 $$ $$ ( 4) + 6 = 2 \qquad (4) + ( 6) = 2 $$ 4. The constant terms in the binomials are $ 4$ and $6$. So, $$ x^2 + 2x 24 = (x 4)(x+6) $$.
Common Questions
What is Example Card: Factoring When c is Negative?
Example Card: Factoring When c is Negative is a key concept in Grade 9 math. It involves applying specific rules and properties to simplify expressions, solve equations, or analyze mathematical relationships. Understanding this topic builds foundational skills needed for higher-level algebra and beyond.
How is Example Card: Factoring When c is Negative used in real-world applications?
Example Card: Factoring When c is Negative appears in practical contexts such as financial calculations, engineering problems, and data analysis. Mastering this skill helps students model and solve problems they will encounter in science, technology, and everyday decision-making situations.
What are common mistakes when working with Example Card: Factoring When c is Negative?
Common errors include forgetting to apply rules to all terms, sign errors when working with negatives, and skipping verification steps. Always double-check by substituting answers back into the original problem and reviewing each algebraic step carefully.