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Chapter 6: Problem 50

Factor each polynomial using the negative of the greatest common factor. $$-15 x^{2}+20$$

Short Answer

Expert verified
\(-5(3x^2 - 4)\)

Step by step solution

01

Identify the GCF

The first step is to identify the greatest common factor (GCF) of \(-15x^2\) and \(20\). In this case, the GCF is \(-5\), without considering the negative sign.
02

Factor out the GCF

After identifying the GCF, the second step is to factor out \(-5\) from each term in the polynomial. This is done by dividing each term in the polynomial by \(-5\). This gives: \(-5(3x^2 - 4)\)
03

Checking the Result

After factoring out the GCF, it's important to check the results by multiplying \(-5\) with each term within the parentheses. If the result matches the original polynomial, the factoring was done correctly: \(-5(3x^2 - 4) = -15x^2 + 20\)

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