Fill in each blank so that the resulting statement is true.
Consider the following long division problem.
StartLongDivision 5 x minus 4 DividedInto 25 x cubed plus 6 x squared plus 11 x minus 6 EndLongDivision
Begin the division process by dividing​ _______ by​ _______, which obtains​ _______. Write this result above​ _______ in the dividend.

To complete the long division problem, we follow these steps:

We are dividing \( 5x - 4 \) into \( 25x^3 + 6x^2 + 11x - 6 \). 

1. **Step 1:** Begin the division by dividing the leading term of the dividend by the leading term of the divisor. This means dividing \( 25x^3 \) by \( 5x \).

   - **Answer for the first blank:** \( 25x^3 \)
   - **Answer for the second blank:** \( 5x \)
   - **Answer for the third blank:** \( 5x^2 \)

2. **Step 2:** Now, write this result, \( 5x^2 \), above the corresponding term in the dividend (which is \( 25x^3 \)).

   - **Answer for the fourth blank:** \( 25x^3 \)

So, the completed sentence is:

"Begin the division process by dividing \( 25x^3 \) by \( 5x \), which obtains \( 5x^2 \). Write this result above \( 25x^3 \) in the dividend."

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Would you like further details or have any questions about the division process?

Here are 5 related questions to deepen your understanding:
1. What is the next step after obtaining \( 5x^2 \) in the long division process?
2. How do you handle subtraction in polynomial long division?
3. What happens when a term in the dividend cancels out completely?
4. Can you explain how to find the remainder in polynomial long division?
5. How does synthetic division differ from polynomial long division?

**Tip:** Always align terms of the same degree when performing long division on polynomials to avoid confusion.

Fill in each blank so that the resulting statement is true. Consider the following long division problem. StartLongDivision 5x - 4 DividedInto 25x^3 + 6x^2 + 11x - 6 EndLongDivision. Begin the division process by dividing​ _______ by​ _______, which obtains​ _______. Write this result above​ _______ in the dividend.

This guide explains how to perform long division on polynomials, specifically dividing 25x^3 + 6x^2 + 11x - 6 by 5x - 4. Learn step-by-step how to divide the leading terms, find the quotient, and subtract to simplify the expression. This method is essential for mastering algebra concepts in Grades 10-12.

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