Example Card: Factoring with a Negative Leading Coefficient
Master Factoring with a Negative Leading Coefficient in Grade 9 Algebra 1. When the leading term is negative, it's a sign to pull out the negative along with the GCF.
Key Concepts
When the leading term is negative, it's a sign to pull out the negative along with the GCF. Let's see how this works.
Example Problem Factor the expression $ 2x^3 10x^2 + 48x$ completely.
Step by Step 1. Notice the leading coefficient is negative ($ 2$). The GCF of the terms is $2x$. To make the new leading term positive, we factor out $ 2x$. 2. Factor out the negative GCF from the expression. Remember that dividing by a negative changes the signs of the remaining terms. $$ 2x^3 10x^2 + 48x = 2x(x^2 + 5x 24) $$ 3. Now, factor the trinomial $x^2 + 5x 24$. We need two numbers that have a product of $ 24$ and a sum of $5$. $$ 8 imes ( 3) = 24 ext{ and } 8 + ( 3) = 5 $$ 4. Use these numbers, $8$ and $ 3$, to write the final factored form, keeping the GCF out front. $$ 2x(x^2 + 5x 24) = 2x(x + 8)(x 3) $$.
Common Questions
What is Factoring with a Negative Leading Coefficient in Algebra 1?
Factoring with a Negative Leading Coefficient is a core Grade 9 Algebra 1 concept covering properties and applications.
How do you work with Factoring with a Negative Leading Coefficient in Grade 9 math?
Factoring with a negative leading term can feel tricky, but there's a simple secret: get that negative number out of the way first! Think of it like taking the trash out before you clean your room. By factoring out the negative GCF (Greatest Common Factor), you turn a complicated problem into a much.
What are common mistakes when learning Factoring with a Negative Leading Coefficient?
Factoring with a negative leading term can feel tricky, but there's a simple secret: get that negative number out of the way first! Think of it like taking the trash out before you clean your room. By factoring out the negative GCF (Greatest Common Factor), you turn a complicated problem into a much friendlier one. Let's break down how to factor .