Use the remainder theorem to find the remainder when f(x) is divided by x+2 whether x+2 is a factor of f(x)
f(x)=2x^6-8x^4+x^2-5
Remainder is=
remainder is=f(-2)
f(-2)=2(-2)^6-8(-2)^4+(-2)^2-5
=-3
so (x+2) is not a factor of f(x)
To find the remainder when f(x) is divided by x+2 using the remainder theorem, we need to evaluate f(-2).
The remainder theorem states that if a polynomial f(x) is divided by x-a, then the remainder is equal to f(a).
So, substitute x = -2 into the polynomial f(x):
f(-2) = 2(-2)^6 - 8(-2)^4 + (-2)^2 - 5
Simplifying the expression:
f(-2) = 2(64) - 8(16) + 4 - 5
f(-2) = 128 - 128 + 4 - 5
f(-2) = -1
Therefore, the remainder when f(x) is divided by x+2 is -1.