# How do you divide (2x^3-x^2+5)÷(x-2)?

Quotient = $2 \cdot {x}^{2} + 3 \cdot x + 6$
Remainder = $17$

#### Explanation:

Without omitting any degrees of the polynomial, the dividend is $2 \cdot {x}^{3} - {x}^{2} + 0 \cdot x + 5$ and the divisor is $x - 2$
Now using the long division method step by step
Q = quotient
R = remainder
Q0 = 0
R0 = $2 \cdot {x}^{3} - {x}^{2} + 0 \cdot x + 5$
Q1 = $2 \cdot {x}^{2}$
R1 = $+ 3 {x}^{2} + 0 \cdot x + 5$
Q2 = $2 \cdot {x}^{2} + 3 x$
R2 = $+ 6 \cdot x + 5$
Q3 = $2 \cdot {x}^{2} + 3 \cdot x + 6$
R3 = $17$