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.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

step-by-step explanation: