Which expression accurately factors 6x² − 18x − 24 after factoring out the GCF?
Understand the Problem
The question is asking which of the provided options correctly factors the quadratic expression 6x² - 18x - 24 after factoring out the greatest common factor (GCF). To solve it, we must first identify and factor out the GCF from the expression, then check which of the options represents the factored form correctly.
Answer
The factored form is $6(x - 4)(x + 1)$.
Answer for screen readers
The correctly factored form of the expression $6x² - 18x - 24$ is:
$$ 6(x - 4)(x + 1) $$
Steps to Solve
- Identify the GCF of the expression To find the GCF of the coefficients in the expression $6x² - 18x - 24$, we need to look at the numbers 6, -18, and -24.
The GCF of 6, 18, and 24 is 6.
- Factor out the GCF from the expression Now we factor out 6 from the original expression:
$$ 6(x² - 3x - 4) $$
- Factor the quadratic expression Next, we need to factor the quadratic expression inside the parentheses, $x² - 3x - 4$. We are looking for two numbers that multiply to -4 and add to -3. The numbers -4 and 1 work.
Thus, we can write:
$$ x² - 3x - 4 = (x - 4)(x + 1) $$
- Combine the factors Now, we combine this result with the GCF we factored out earlier:
$$ 6(x - 4)(x + 1) $$
Thus, the complete factored form of the provided quadratic expression is:
$$ 6(x - 4)(x + 1) $$
The correctly factored form of the expression $6x² - 18x - 24$ is:
$$ 6(x - 4)(x + 1) $$
More Information
Factoring quadratics is a key skill in algebra, allowing us to simplify expressions or solve equations. Factoring by taking out the GCF first can save time and help avoid mistakes in working with the remaining quadratic.
Tips
- Forgetting to factor out the GCF before trying to factor the quadratic expression. Always start by finding the GCF to simplify the problem.
- Not identifying the correct numbers that multiply to the constant term and add to the coefficient of the linear term when factoring the quadratic.
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