Question 282871
To find the zeros means to find the number(s) that when replaced for the given x in your polynomial function, will create zero for the function.  In other words, we need to find numbers (or maybe just one number) that when used in place of every x in your function, zero is the result.

We can use synthetic division to find our zero(s).

See the video clip to learn about synthetic division.

http://www.youtube.com/watch?v=HY2UylGTDYU

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Back to your question.

I will use synthetic division on paper until finding one number or group of numbers that will give me a zero remainder.

List the factors of the leading coefficient and the constant.

Factor of 1 = 1

Factors of 4 = 1, 2, and 4

We now divide the constant's factors by the factor of the leading coefficient.

±1/1, ±2/1 and ±4/1 = ±1, ±2 and ±4

After using synthetic division, I found the only zero to be x = 4.

In other words, if you replace x with 4 in your function, you will get zero on both sides of the equation.

Why don't you try it?

0 = (4)^3 - 4(4)^2 + 4 - 4...After doing the math, the right side should also produce zero.

I'll let you do the math.

The x-intercept of any function is the location where the graph of the function crosses the x-axis.  So, there is a relationship between the x-intercepts and the zeros.  In fact, the x-intercepts = the roots = the solution = the zeros.