What should be added in the polynomial x³ + 2x² – 9x + 1 so that it is completely divisible by x + 4?

Let p(x) = x³ + 2x² – 9x + 1

And g(x) = x + 4

Now put g(x) = 0

X + 4 = 0

X = –4

So remainder of p(x) when divided by g(x) = p(–4)

P(–4) = (–4)³ + 2(–4)² – 9(–4) + 1

P(– 4) = –64 + 32 + 36 + 1

P(– 4) = 5

∴ – 5 should be added to p(x) so that p(x) is completely divisible by x + 4.