Since f(-7) is not equal to zero, x + 7 is not a factor of the polynomial f(x), indicating it is not a root of the equation.
To determine whether the binomial x + 7 is a factor of the polynomial function f(x) = 2x^3 + 16x^2 - 4x - 50, you can use the factor theorem. According to the factor theorem, if f(c) = 0, where c is the root of the binomial, then x - c is a factor of f(x).
To check this, substitute x = -7 into the polynomial function:
f(-7) = 2(-7)^3 + 16(-7)^2 - 4(-7) - 50
Calculating this expression will tell us if x + 7 is a factor. If f(-7) = 0, then x + 7 is a factor.
f(-7) = 2(-343) + 16(49) + 28 - 50
f(-7) = -686 + 784 - 22
f(-7) = 76
Since f(-7) is not equal to zero, x + 7 is not a factor of the polynomial f(x). In other words, the binomial x + 7 does not evenly divide f(x) and is not a root of the polynomial equation.
Complete question:
Determine whether the binomial is a factor of the polynomial function.
f(x) = 2x^3 + 16x^2 - 4x - 50; x + 7