Factoring with fractions involves identifying a common fractional factor within a polynomial and extracting it to simplify the expression. Let's explore how to do this, incorporating insights from the provided reference.
Here's a breakdown of the process:
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Identify the Common Fraction: Look for a fraction that is a common factor of all terms in the expression.
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Factor Out the Fraction: Extract the common fraction from each term. This involves dividing each term by the fraction. When you divide by a fraction, it's the same as multiplying by its reciprocal.
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Simplify: After factoring out the fraction, simplify the remaining terms inside the parentheses.
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Double-Check: According to the YouTube video, ensure that if you were to multiply the factored expression back together, you would obtain the original trinomial. Also, don't forget to bring down the fraction.
Example:
Let's say you have the expression: (1/2)x + (1/2).
- The common fraction is 1/2.
- Factoring out 1/2, you get: (1/2)(x + 1)
More Complex Example (Inspired by the Reference):
Imagine you need to factor an expression that results from a previous step, such as: (1/4)(3x + 2).
- In this case, (1/4) is already factored out. The key is to remember this factor and not lose track of it.
- If you were to expand this, you'd multiply (1/4) by both 3x and 2, resulting in (3/4)x + (2/4) which simplifies to (3/4)x + (1/2).
Key Considerations:
- Verification: Always multiply the factored expression back to ensure it matches the original.
- Careful Division: Dividing by a fraction correctly is crucial. Remember to multiply by the reciprocal.
