To find the first step of the division problem [tex]\(\left(8 x^3 - x^2 + 6 x + 7\right) \div (2 x - 1)\)[/tex], we need to focus on the leading terms of the polynomials.
1. Identify the leading term of the numerator: [tex]\(8 x^3\)[/tex].
2. Identify the leading term of the denominator: [tex]\(2 x\)[/tex].
3. Perform the division of the leading term of the numerator by the leading term of the denominator.
To compute this step:
[tex]\[ \frac{8 x^3}{2 x} \][/tex]
Divide the coefficients and subtract the exponents of [tex]\(x\)[/tex]:
[tex]\[ \frac{8}{2} \cdot \frac{x^3}{x} = 4 \cdot x^{3-1} = 4 x^2 \][/tex]
Therefore, the first step in this division problem is:
[tex]\[ \frac{8 x^3}{2 x} = 4 x^2 \][/tex]
So the correct answer is:
Divide [tex]\(8 x^3\)[/tex] by [tex]\(2 x\)[/tex].
