Rational root theorem

Question

what would the remainder be if (2x^134-7x^45+x^9-4) is divided by (x+1) ?

Answer 1

Alternatively, do synthetic division, putting -1 into the division slot at the left. 

Answer 2

Let f(x) = 2x¹³⁴ - 7x⁴⁵ + x⁹ - 4

 

x+1 = x - (-1)

 

By the Remainder Theorem, the remainder when f(x) is divided by x+1 is f(-1)

 

f(-1) = 2(-1)¹³⁴ - 7(-1)⁴⁵ + (-1)⁹ - 4 = 2 + 7 - 1 - 4 = 4