# How do you divide y^4-8y^3+10y^2+2y+4 by y-2 and is it a factor of the polynomial?

${2}^{4} - 8 \cdot {2}^{3} + 10 \cdot {2}^{2} + 2 \cdot 2 + 4$
$= 16 - 64 + 40 + 4 + 4 = 0$
Since $f \left(2\right)$ is $0$, the linear function $y - 2$ is a factor.
As for the quotient, long division can be employed to give ${y}^{3} - 6 {y}^{2} - 2 y - 2$