IS (x-2) a factor of
f(x)= -9x^4+16x^3+8x^2-9x+2
To determine if (x-2) is a factor of f(x), we need to use the remainder theorem. According to this theorem, if f(a) equals zero when we substitute a value for x in the polynomial f(x), then (x-a) is a factor of f(x).
In this case, we need to substitute the value 2 for x in the polynomial f(x) and check if the result is zero.
Let's compute f(2):
f(x) = -9x^4 + 16x^3 + 8x^2 - 9x + 2
f(2) = -9(2)^4 + 16(2)^3 + 8(2)^2 - 9(2) + 2
= -9(16) + 16(8) + 8(4) - 18 + 2
= -144 + 128 + 32 - 18 + 2
= 0
Since f(2) is equal to zero, we can conclude that (x-2) is a factor of f(x).