if a polynomial is being divided by x+6 using synthetic division what value goes in the far left box

When using synthetic division to divide a polynomial by \( x + 6 \), the value that goes in the far left box is the **opposite** of the constant term in \( x + 6 \). Since the divisor is \( x + 6 \), you take the opposite of \( +6 \), which is \( -6 \). 

So, the value that goes in the far left box is **-6**.

Would you like more details on the synthetic division process or have any other questions?

Here are five related questions you might find interesting:

1. How does synthetic division differ from long division of polynomials?
2. What happens if the divisor is \( x - 6 \) instead of \( x + 6 \)?
3. Can synthetic division be used to divide by a quadratic divisor?
4. What do the numbers below the line in synthetic division represent?
5. How can synthetic division help in finding polynomial roots?

**Tip:** Always remember to change the sign of the constant term in the divisor before starting synthetic division!

Discover how to use synthetic division to divide a polynomial by x + 6. Understand the process step-by-step, including identifying the value for the far left box. Suitable for high school students studying polynomial division.

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