How to factor an expression using GCF?
Understand the Problem
The question is asking for a method to factor an algebraic expression by using the greatest common factor (GCF). This involves identifying the GCF of the terms in the expression and factoring it out to simplify the expression.
Answer
The factored form of the expression $6x^2 + 9x$ is $3x(2x + 3)$.
Answer for screen readers
The factored form of the expression $6x^2 + 9x$ is $3x(2x + 3)$.
Steps to Solve
- Identify the terms of the expression
Break down the given algebraic expression into its individual terms. For example, if the expression is $6x^2 + 9x$, the terms are $6x^2$ and $9x$.
- Find the GCF of the coefficients
Determine the greatest common factor of the coefficients of the terms. In our example, the coefficients are 6 and 9. The GCF of 6 and 9 is 3.
- Identify the variable part
Look at the variables in the expression. In this case, both terms contain the variable $x$. The smallest power of $x$ in the terms needs to be taken into account, which, here, is $x^1$.
- Combine the GCF
Now combine the GCF of the coefficients and variable part to get the overall GCF. So from our example: $$ GCF = 3x $$
- Factor the expression
Divide each term by the overall GCF and express the original expression as the product of the GCF and the remaining polynomial. For our example, we divide:
- $6x^2 ÷ 3x = 2x$
- $9x ÷ 3x = 3$
Thus, the expression becomes: $$ 6x^2 + 9x = 3x(2x + 3) $$
The factored form of the expression $6x^2 + 9x$ is $3x(2x + 3)$.
More Information
Factoring out the GCF helps simplify expressions and is a crucial step in solving polynomial equations. Understanding how to find the GCF is also helpful in reducing fractions and finding equivalent expressions.
Tips
- Forgetting to check for a GCF when the terms contain only variables.
- Not including all the variables when determining the GCF.
- Confusing the numerical GCF with the overall GCF that includes variable parts.
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