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Synthetic division,Remainder factor theorem, graphing cubic

1. Explain what synthetic division is and what it is used for. (include at least 2 different uses for synthetic division) Give an example of synthetic division, show all steps. Explain what your answer means.

2. Pick a cubic function. (use something not too simple. a good example: y = 2(x+1)^3 - 5) Starting with y = x^3, use vertical and horizontal translations, as well as, shrinking and stretching to graph your function. (make sure to explain in English what you are doing as well as graphing y = x^3 and your function) Using an algebraic method, find the roots of your function. Describe the symmetry of your function. Explain the concept of symmetry in general. (which functions are symmetric, which are not. how can you tell from the equation?)

3. State and explain (in simple English) what Remainder and Factor Theorems mean.

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Please find the solution/explanation attached herewith.

1. Explain what synthetic division is and what it is used for. (include at least 2 different uses for synthetic division) Give an example of synthetic division, show all steps. Explain what your answer means.

Synthetic division is a shortcut method for dividing a polynomial by a linear factor of the form x + a or x - a.

Synthetic division can also be used in conjunction with the "Remainder Theorem" to find the value of a polynomial at a real value.

Example:

Let us take the polynomial 3x^2 + 4x + 4 divided by x - 1

Next, all the variables and their exponents ( , ) are removed, leaving only a list of the coefficients: 3, 4, 4. These numbers form the dividend. We form the divisor for the synthetic division using only the constant term (1) of the linear factor as shown below:

The first number in the dividend 3 is put into the first position of the result area ...

Solution Summary

A step-by-step explanation are provided for synthetic division, graphing cubic functions using transformations, and remainder factor theorem.

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