Determine whether x+6 is a factor of x^3+4x^2-27x-90
perform a synthetic division or algebraic long division.
yes, it is a factor
To determine whether x+6 is a factor of x^3+4x^2-27x-90, we can use the Remainder Theorem.
The Remainder Theorem states that if a polynomial f(x) is divided by x - a, the remainder is equal to f(a).
In this case, we want to check if x+6 is a factor, so we need to test whether the given polynomial is divisible by x+6.
To do this, substitute -6 for x in the polynomial:
f(-6) = (-6)^3 + 4(-6)^2 - 27(-6) - 90
Calculate the result:
f(-6) = -216 + 144 + 162 - 90 = 0
If the result is equal to 0, it means that x+6 is a factor of the polynomial. Otherwise, it is not a factor.
In this case, since f(-6) = 0, x+6 is indeed a factor of x^3+4x^2-27x-90.