Question

When f(x) = x4 + x2 – 4x + 6 is divided by ( x + 1) , the remainder is
(A) 10 (B) 0
(C) 12 (D) 8

Answer 1

C

Answer 2

Can you explain ?

Answer 3

Substitute x=-1 into the polynomial, i.e. evaluate f(-1) and that would be the remainder.

Answer 4

x=-1 comes from the factor (x+1)=0, so
f(-1) = (-1)^4 + (-1)^2 – 4(-1) + 6 = 12

Answer 5

whatever
\[f(-1)\] is

Answer 6

Why (x+1) should be 0 ?

Answer 7

http://en.wikipedia.org/wiki/Polynomial_remainder_theorem

Answer 8

when the polynomial is divided by (x+1) we get a remainder of zero, which means the polynomial can be written in the form\[P(x)(x+1)=f(x)\]so if you wanted the zero's of f(x), x=-1 would be one of them, but there is nothing in the problem to suggest that since the polynomial is a function and not equal to zero.

Answer 9

P(x) is the polynomial that you get after dividing by (x+1)

Answer 10

\[f(x) = x4 + x2 – 4x + 6=(x+1)\times (\text{ something}) + \text{remainder}\]
\[f(-1)=(-1+1)\times (\text{ something}) + \text{remainder}\]
\[f(-1)=(0)\times (\text{ something}) + \text{remainder}\]
\[f(-1)=\text{ remainder}\]

Answer 11

can you do synthetic division @abdul shabeer?

Answer 12

What does that mean ?

Answer 13

Nice @satellite! :)

Answer 14

it's a fast way of dividing polynomials by expressions of the form (x-a)
if I divide some polynomial P(x) by (x-a) and get no remainder, then a is a root of the equation.
http://www.purplemath.com/modules/synthdiv.htm

Answer 15

Yes, I know this division

Answer 16

12