Question

Use the Factor Theorem to determine if
x - 3 is a factor of f(x) = x4 - 8x3 - 45x2 + 524x - 1120.

Answer 1

Factor theorem says that if (x-r) is a factor of a polynomial P(x), the value of P(r) = 0. In other words, plug x = 3 into the polynomial and evaluate the result. If it is 0, then (x-3) is a factor of the polynomial (and x = 3 is a root of the polynomial).

Answer 2

so is x - 3 is a factor of f(x)?

Answer 3

Well, what do you get when you evaluate \(f(3) = (3)^4-8(3)^3-45(3)^2+524(3)-1120\)
?

Answer 4

If that is 0, then (x-3) is a factor. If it is not 0, (x-3) is not a factor.