# How do you divide (2k^3-13k^2-77k+60)div(k-10) using synthetic division?

Mar 6, 2018

Quotient is $2 {k}^{2} + 7 k - 7$ and remainder is $- 10$

#### Explanation:

$2 {k}^{3} - 13 {k}^{2} - 77 k + 60$

=$2 {k}^{3} - 20 {k}^{2} + 7 {k}^{2} - 70 k - 7 k + 70 - 10$

=$2 {k}^{2} \cdot \left(k - 10\right) + 7 k \cdot \left(k - 10\right) - 7 \cdot \left(k - 10\right) - 10$

=$\left(2 {k}^{2} + 7 k - 7\right) \cdot \left(k - 10\right) - 10$

Hence quotient is $2 {k}^{2} + 7 k - 7$ and remainder is $- 10$