Use remainder theorem to find the remainder when f(x) is divided by x-c. Then use the factor them to determine if x-c is a factor of f(x)

Question

f(x)=3x^4+x^3-3x+1,x+1/3

Answer 1

Greeting! Lets solve this shall we ?

So, we must find out if (x-c) is a factor of this polynomial f(x) = 3x⁴+x³ - 3x + 1, where (x-c) = (x+1/3). Notice that (x+1/3) is a zero at x = -1/3. We now plug in -1/3 for x such that

f(-1/3) = 3(-1/3)⁴ + (-1/3)³ - 3(-1/3) + 1 = 2 after simplification of the fractions. This means that 2 is the remainder when dividing the polynomial by x+(1/3).

Therefore, (x+1/3) is not a factor of f(x) because we did not get f(-1/3) = 0.

I hope this helped!