Find the values of a, x^4-3x^2+2x+a is divisible by x+1?

If remainder is zero when f(x) is divided by (x + a), then f(-a) = 0

f(x) = x^4 - 3x^2 + 2x + a

f(-1) = 1 - 3 -2 + a = 0

=> -4 + a = 0

a = 4

Use polynomial long division (or synthetic division, if you're comfortable with it). Just don't forget to include 0*x^3 when you write out the dividend. The concept is really the same one you've been using in ordinary long division since the 3rd grade, only you never bothered to write the dividend out as a sum of terms. For instance, when you divided 1023 by 11, you didn't write the dividend as 1000 + 20 +3 or the divisor as 10 + 1. That's really all you're doing with polynomial division.

You'll find that a is a nice, friendly integer.