What is the first step of the following division problem?

(8*x*3 – *x*2 + 6*x* + 7) ÷ (2*x* – 1)


Divide 8*x*3 by 2*x.*

Divide 2*x* by 8*x*3.

Divide 6*x* by 2*x.*

Divide 2*x* by 6*x.*

The division problem is:

\[
\frac{8x^3 - x^2 + 6x + 7}{2x - 1}
\]

The first step in dividing polynomials using long division is to divide the leading term of the dividend by the leading term of the divisor. In this case:

- The leading term of the dividend is \( 8x^3 \).
- The leading term of the divisor is \( 2x \).

Now, divide:

\[
\frac{8x^3}{2x} = 4x^2
\]

So, the correct first step is:

**Divide \( 8x^3 \) by \( 2x \)**, which gives \( 4x^2 \).

Would you like to proceed with the remaining steps or have further details about this process?

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Here are 5 questions to deepen your understanding:
1. What is the next step after dividing the leading terms in polynomial division?
2. How do you handle subtraction during polynomial long division?
3. Can polynomial long division result in a remainder?
4. How do you identify the quotient and remainder after completing the division?
5. How would synthetic division work for this specific example?

**Tip:** Always align terms with similar powers when performing polynomial long division to avoid confusion during subtraction.

What is the first step of the following division problem? (8*x*3 – *x*2 + 6*x* + 7) ÷ (2*x* – 1)

Learn how to solve the polynomial division problem (8x^3 – x^2 + 6x + 7) ÷ (2x – 1) step-by-step. This detailed guide covers dividing the leading terms and provides insights into polynomial long division. Suitable for high school students in Grades 9-12.

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