Question

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

Answer 1

Using factor theorem:

`2^4-8*2^3+10*2^2+2*2+4`
`=16-64+40+4+4 = 0`

Since `f(2)` is `0`, the linear function `y-2` is a factor.

As for the quotient, long division can be employed to give `y^3-6y^2-2y-2`