Find the reminder when f(x)=2x^19-7x is divided by x+1

Question

what Is the remainder from that equation

Answer 1

Two methods possible: long division or the remainder theorem. Long division takes patience, the remainder must have a power lower than the divisor.

Remainder theorem states that the remainder when F(x) is divided by (x-a) is F(a).

for (x+1), a = -1 so

Remainder = f(-1) =2(-1)¹⁹ -7(-1) =-2+7 =5.

Answer 2

-9x is the remainder

2x^19 -7x divided by x+1 = 2x^18-2x^17 + ..... +2x^2-2x descending powers with alternating signs

ending in -2x and -remainder of -9x/(x+1)

Answer 3

By the Remainder Theorem, the remainder when a polynomial function f(x) is divided by x - c is f(c).

Since x + 1 = x - (-1), the remainder is f(-1) = 5.