Question

divide. if there is no remainder, enter the quotient. if there is a remainder, enter your answer as quotient+\frac{remainder}{divisor}.\
ewline \left(2x^3 + 3x - 5\
ight) \div \left(x - 1\
ight)

Explanation:

Step1: Set up polynomial long division

Divide $2x^3 + 0x^2 + 3x - 5$ by $x-1$ (insert $0x^2$ for missing term).

Step2: Divide leading terms

$\frac{2x^3}{x} = 2x^2$. Multiply $(x-1)$ by $2x^2$: $2x^3 - 2x^2$.
Subtract from dividend:
$$(2x^3 + 0x^2 + 3x - 5) - (2x^3 - 2x^2) = 2x^2 + 3x - 5$$

Step3: Divide new leading terms

$\frac{2x^2}{x} = 2x$. Multiply $(x-1)$ by $2x$: $2x^2 - 2x$.
Subtract:
$$(2x^2 + 3x - 5) - (2x^2 - 2x) = 5x - 5$$

Step4: Divide leading terms again

$\frac{5x}{x} = 5$. Multiply $(x-1)$ by $5$: $5x - 5$.
Subtract:
$$(5x - 5) - (5x - 5) = 0$$

Answer:

$2x^2 + 2x + 5$