Is the binomial a factor of the polynomial function? f(x)=x3+4x2−9x−36 yes no (x−1) (x−3) (x+3) (x−4) (x+4)

The given polynomial is
f(x) = x³ + 4x² - 9x - 36

According to the Remainder Theorem, if (x-a) is a factor of f(x), then x=a is a zero, and f(a) = 0.

Let us text the given factors.
(x-1):
f(1) = 1³ + 4(1²) - 9(1) - 36 = -22            NO

(x-3):
f(3) = 3³ + 4(3²( - 9*3 - 36 = 54          NO

(x+3):
f(-3)= (-3)³ + 4(-3)² -9(-3) - 36 = -54   NO

(x-4):
f(4) = 4³ + 4(4²) - 9(4) - 36 = 128        NO

(x+4):
f(-4) = (-4)³ + 4(-4)² - 9(-4) - 36 = -72   NO

The graph confirms that none of the given binomials is a factor.

None of the given binomials is a factor.