Question 175312
f(x)= x^4+8x^3+12x^2; g(x) = x + 1

I will do the above question and you can do the next one.

Do you see x + 1 as the value for the function g?

You will notice that the quantity has a +1, right?

Let x = the opposite of +1, which is -1.

Everywhere there is an x, replace it with -1 and simplify the polynomial function f.

So, x = -1

f(-1) = (-1)^4 + 8(-1)^3 + 12(-1)^2

f(-1) = 1 - 8 + 12

f(-1) = -7 + 12

f(-1) = 5

The remainder is 5.

This is the basic idea behind the Remainder Theorem.

Do the same with the other polynomial function.

Understood?