find the greatest common factor of x**2+8x-20=0

To find the greatest common factor (GCF) of the quadratic expression \(x^2 + 8x - 20 = 0\), first, observe that we are not factoring the equation directly, but seeking the GCF of the terms involved.

The expression is:

\[
x^2 + 8x - 20
\]

The GCF is the largest expression that divides each term of the quadratic expression evenly. Let's break it down:

1. \(x^2\) has a factor of \(x\),
2. \(8x\) also has a factor of \(x\),
3. \(-20\) has no factor of \(x\), only numerical factors.

Since \(-20\) doesn't have \(x\) as a factor, the greatest common factor between the three terms is **1**.

Thus, the GCF of the expression \(x^2 + 8x - 20\) is **1**.

Would you like more details or a different approach? Here are some related questions for further exploration:

1. How do you factor the quadratic \(x^2 + 8x - 20\)?
2. How do you solve the quadratic equation \(x^2 + 8x - 20 = 0\)?
3. What is the difference between the GCF and the factors of a quadratic equation?
4. Can the GCF ever be a variable term in quadratic equations?
5. What is the significance of finding the GCF in polynomials?

**Tip**: When looking for the GCF, always start by identifying the highest common factors for both variables and constants separately.

Find the greatest common factor of x^2 + 8x - 20 = 0

Learn how to find the greatest common factor (GCF) of the quadratic equation x^2 + 8x - 20. This problem breaks down the key algebraic concepts involved, including identifying common factors and recognizing that the GCF is 1. Suitable for students in Grades 7-9.

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