Example Card: Factoring with a Sign Change
Factor trinomials that require a sign change in Grade 9 Algebra. Pay careful attention to signs when choosing factor pairs that sum to the middle coefficient.
Key Concepts
Sometimes the terms aren't in a convenient order. Let's see how rearranging and a clever sign change can reveal the solution. This example highlights the key idea of factoring a four term polynomial.
Example Problem Factor the expression $2x^2y 10x + 15 3xy$ completely.
Step by Step 1. Group the terms into two binomials. Notice the initial grouping reveals binomials that are opposites. $$ (2x^2y 10x) + (15 3xy) $$ 2. Factor the Greatest Common Factor (GCF) from each binomial. $$ 2x(xy 5) + 3(5 xy) $$ 3. To make the binomials match, factor out a $ 1$ from the second term. Remember that $5 xy$ is the same as $ 1(xy 5)$. $$ 2x(xy 5) + 3( 1)(xy 5) $$ 4. Simplify the expression. $$ 2x(xy 5) 3(xy 5) $$ 5. Now, factor out the common binomial factor, $(xy 5)$. $$ (xy 5)(2x 3) $$.
Common Questions
What is Example Card: Factoring with a Sign Change in Grade 9 Algebra?
Let's see how rearranging and a clever sign change can reveal the solution Mastering this concept builds a foundation for advanced algebra topics.
How do you approach Example Card: Factoring with a Sign Change problems step by step?
This example highlights the key idea of factoring a four-term polynomial Use this method consistently to avoid common errors.
What is a common mistake when studying Example Card: Factoring with a Sign Change?
Notice the initial grouping reveals binomials that are opposites Always check your work by substituting back into the original problem.