PLS HELP ASAP!! One factor of the function f(x) = x3 − 8x2 + 17x − 10 is (x − 5). 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.

Our x-intercepts are at:

Our y-intercept is (0, -10).

Step-by-step explanation:

We have the function:

And we know that one factor is:

Since we know one factor, we can use synthetic division to find the depressed polynomial, then continue factoring to find the remaining zeros (x-intercepts).

To find the y-intercept, we can simply substitute 0 for x and evaluate. This can be done anytime.

We can apply synthetic division for a polynomial P(x) divided by a binomial in the form (x-a).

Since our factor is (x-5), a=5.

Please refer to the attachment below for the synthetic division.

So, we are left with:

The remaining factor is now a quadratic. This can be easily factored:

To find our zeros, set our function f(x) to 0:

Then by the Zero Product Property:

Hence, our x-intercepts are:

To find our y-intercept, we can substitute 0 for x and evaluate. Hence:

Evaluate:

So, our y-intercept is at (0, -10).

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6