Question

digits are divided. use the same process to divide polynomials.

set up the division as a long-division problem
\\(x-5 \overline{) x^2 + 3x - 40}\\)

next, divide the first term in the dividend by the first term in the divisor. divide \\(x^2 \div x\\).
\\(x-5 \overline{) x^2 + 3x - 40}\\)

multiply the quotient by the divisor. multiply \\(x \cdot (x - 5)\\).
\\(x-5 \overline{) x^2 + 3x - 40}\\)
\\(x^2 - 5x\\)

subtract and bring down the next term.
\\(x-5 \overline{) x^2 + 3x - 40}\\)
\\(-(x^2 - 5x)\\)
\\(8x - 40\\)

now divide the first term in this expression by the first term in the divisor. divide \\(8x \div x\\).
\\(x-5 \overline{) x^2 + 3x - 40}\\)
\\(-(x^2 - 5x)\\)
\\(8x - 40\\)

Explanation:

Divide the first term of the remainder by the divisor

Using the Polynomial Long Division knowledge point

$$ \frac{8x}{x} = 8 $$

Answer:

Now divide the first term in this expression by the first term in the divisor. Divide \(8x \div x\).

The value that goes in the box is <blank>8</blank>.