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.

Answer:

None of the given binomials is a factor.