Example Card: Factoring Out the GCF to Find Roots
Solve factoring out the gcf to find roots in Grade 9 math — Sometimes the greatest common factor is hiding in plain sight. Part of Systems and Problem Solving for Grade 9.
Key Concepts
Sometimes the greatest common factor is hiding in plain sight. Let's practice another key idea from this lesson: Finding the Roots by Factoring Out the GCF .
Example Problem Find the roots of the equation $3x^2 = 24x 48$.
Step by Step 1. First, set the equation equal to zero by moving all terms to one side. $$3x^2 + 24x + 48 = 0$$ 2. We can see that all terms are divisible by 3. Let's factor out the Greatest Common Factor (GCF), which is 3. $$3(x^2 + 8x + 16) = 0$$ 3. Now, factor the trinomial expression inside the parentheses. This is a perfect square trinomial. $$3(x+4)(x+4) = 0$$ 4. The constant factor 3 can be disregarded since it can never equal 0. The factor $(x+4)$ appears twice, but we only need to set it equal to zero once. $$x + 4 = 0$$ 5. Solve for $x$. $$x = 4$$ 6. Check the solution in the original equation. $$ \begin{align } 3x^2 &= 24x 48 \\ 3( 4)^2 &\stackrel{?}{=} 24( 4) 48 \\ 3(16) &\stackrel{?}{=} 96 48 \\ 48 &= 48 \quad \checkmark \end{align } $$ The root is 5.
Common Questions
What is 'Factoring Out the GCF to Find Roots' in Grade 9 math?
Sometimes the greatest common factor is hiding in plain sight. Let's practice another key idea from this lesson: Finding the Roots by Factoring Out the GCF.
How do you solve problems involving 'Factoring Out the GCF to Find Roots'?
Let's practice another key idea from this lesson: Finding the Roots by Factoring Out the GCF. First, set the equation equal to zero by moving all terms to one side.
Why is 'Factoring Out the GCF to Find Roots' an important Grade 9 math skill?
For $(3y^4)^2$, many people correctly get $y^8$ but forget to square the 3, resulting in an incorrect answer of $3y^8$.. Always distribute the power to every part inside the parentheses!.