Just carry out long division. P(x) is the quotient, k is the remainder. Divide by x+1

Alternatively, you can split out or rewrite the terms such that (x + 1) can be factored out.

I've shown this earlier but apparently your earlier post has been deleted.

f(x) = 2x³ - 12x² + 17x + 3

= 2x³ + 2x² - 14x² + 17x + 3

= 2x²(x + 1) - 14x² - 14x + 31x + 3

= 2x²(x + 1) - 14x(x + 1) + 31x + 31 - 28

= 2x²(x + 1) - 14x(x + 1) + 31(x + 1) - 28

Now we can factor out (x + 1)

= (x + 1)(2x² - 14x + 31) - 28

P(x) = 2x² - 14x + 31
k = -28