# How do you find the quotient of 3x^3 - 2x^2 +5 / x - 4?

Dec 22, 2015

$3 {x}^{2} + 10 x + 40$

#### Explanation:

divide the term $3 {x}^{3} - 2 {x}^{2} + 5$ traditionally by $x - 4$
so you have $3 {x}^{3} - 2 {x}^{2} + 5$ = $x - 4 \cdot$ quotient + remainder

1. $x - 4 \cdot 3 {x}^{2} = 3 {x}^{3} - 12 {x}^{2}$
2. Subtract this with the polynomial you get $10 {x}^{2} + 5$
3. $x - 4 \cdot 10 x = 10 {x}^{2} - 40 x$
4. Subtract this from the polynomial in step 2 to get $40 x + 5$
5. $x - 4 \cdot 40 = 40 x - 160$
6. Subtract this from the polynomial in step 4 to get $165$

now the number cannot be divided further hence 165 is remainder
and $3 {x}^{2} + 10 x + 40$ is the quotient (sum of terms we used in steps 1, 3 and 5)

$3 {x}^{3} - 2 {x}^{2} + 5 = \left(x - 4\right) \cdot \left(3 {x}^{2} + 10 x + 40\right) + 165$