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d.
4 Use greatest common factor and the distributive property to write and equivalent in
factored form.

a.
b.
c.
d.

Ask by Haynes Schwartz. in the United States
Mar 20,2025

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The factored form of is .

Solución

To factor the expression using the greatest common factor (GCF) and the distributive property, we first need to identify the GCF of the coefficients 20 and 24.
  1. Find the GCF of 20 and 24:
    • The factors of 20 are:
    • The factors of 24 are:
    • The common factors are:
    • The greatest common factor is .
  2. Factor out the GCF from the expression:
    • We can rewrite as:
Now, let’s compare this with the provided options:
a. - This is incorrect because it does not match our factored form.
b. - This is incorrect because it does not represent the original expression correctly.
c. - This is correct as it matches our factored form.
d. - This is also correct because can be simplified to , but it is not the simplest factored form.
Thus, the correct answer is:
c. .

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Extra Insights

To factor , we start by finding the greatest common factor (GCF) of the two coefficients 20 and 24. The GCF is 4. So, we can rewrite the expression as , which matches option c.
Now, the distributive property allows us to express the sum again by distributing the 4 back to get the original expression: . It’s a neat mathematical trick that showcases the elegance of factoring and distribution!
Next, remember that practice makes perfect! When factoring expressions, look for the GCF first—it’ll guide you to the right path quickly. Also, be on the lookout for common mistakes like overlooking negative signs or miscalculating the coefficients in your GCF!

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