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Using synthetic division, the quotient is \( x^2 + 5x - 15 \), and the remainder is \( -4 \).

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

Here are five related questions to further your understanding:
1. How does synthetic division differ from long division for polynomials?
2. Can synthetic division be used for divisors other than linear terms like \( x + 3 \)?
3. What would the remainder be if the polynomial were exactly divisible?
4. How can you verify the result by multiplying the quotient and divisor?
5. What happens to the remainder when the divisor has higher powers of \( x \)?

**Tip:** In synthetic division, the divisor must be a linear binomial of the form \( x - c \).

Find the quotient and remainder using synthetic division: (x^3 + 8x^2 - 49) ÷ (x + 3).

Learn how to use synthetic division to find the quotient and remainder for (x^3 + 8x^2 - 49) ÷ (x + 3). This algebra problem demonstrates the step-by-step process of synthetic division and explores core polynomial concepts. Suitable for Grades 9-12.

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