Will give !

factor completely 9x3 + 36x2 − x − 4.

a. (3x + 4)(3x − 4)(x + 1)

b. (3x + 1)(3x − 1)(x + 4)

c. (9x^2 − 1)(x + 4)

d. (3x + 1)(3x − 1)(x − 4)

B. (3x + 1)(3x − 1)(x + 4)  

Step-by-step explanation:

1. Use the rational roots theorem to find a root.

The general formula for a third-degree polynomial is

f(x) = ax³ + bx² + cx + 3

Your polynomial is  

ƒ(x) = 9x³ + 36x² − x − 4

a = 9; d = -4

According to the Rational Roots Theorem, the possible rational roots are the factors of d divided by the factors of a.

Factors of d = ±1, ±2, ±4,  

Factors of a = ±1, ±3, ±9

This gives us 20 possible roots ranging from x = -4 to x = 4.

Let's try x = -4.

f(-4) = 9(-4)³ + 36(-4)² − (-4) − 4 = 9(-64) + 36(16) + 4 - 4 = -576 + 576 =0

So, x = -4 is a root, and (x+ 4) is a factor of the polynomial

2. Use synthetic division to discover the other factors

Divide the polynomial by (x+4).

So, (9x² - 1) is another factor

3. Factor the quadratic.

9x² - 1 = (3x + 1)(3x - 1)

4. Write the complete factorization

ƒ(x) = (x + 4)(3x + 1)(3x - 1)

The figure below shows the graph of your function. with zeros at -4, -⅓, and ⅓.

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step-by-step explanation:

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step-by-step explanation:

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