One factor of the function f(x) = x3 - 6x² + 11x - 6 is (x-3). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer.

Step-by-step explanation:

Let's start with the easiest way to answer something like this. Graph it.

The graph was put in as y = x^3 - 6x^2 + 11x - 6

The roots need to multiply to - 6 if the equation has integer roots (which it does). The y intercept is (-6,0).

Oh, I just saw that you can't use technology. Well you might use it to get the answer.

(x - 3) || x^3 - 6x^2 + 11x - 6 || x^2 - 3x + 2

            x^3 - 3x^2

                   -3 x^2  + 11x    

                  -3 x^2 +  9x

                                   2x  - 6    

                                   2x  - 6

Now x^2 - 3x + 2     factors

(x - 2)(x - 1)

So your three factors are (x - 3)(x - 2)(x - 1)

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~

it is 570

step-by-step explanation: