Perform the following polynomials divisions using long/synthetic divisionin Mathematics by Euler
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A+ TUTORIAL FOR THE FOLLOWING QUESTIONS
Functions and Differences
The following questions are to be answered with full solutions. Be sure to focus on proper mathematical form, including:
1.One equal sign per line
2.Equal signs in each question lined up vertically with each other
3.No self-developed short form notations
4.One step or idea per line (do not do steps in your head that are not written down, each line must show a step-by-step progression from question to answer)
5.All graphs must be done by hand. Do not use graphing software to create any graphs.
Assessment OF Learning: Polynomial Funcs Mid-Unit Assignment
1.Perform the following polynomials divisions using long/synthetic division:
a.(x2 - 7x - 12) (x + 2)
b.(x3 + x2 3x + 1) (x 1)
c.(3x3 + 5x2 3x 5) (x + 1)
d.(x4 - 3x3 + 3x + 2) (x - 2)
2.Complete the following:
a.Based on the results of question 1, what do you notice when the divisor is a factor of the polynomial?
b.x2 a2 is called a difference of squares. Assuming one factor (the divisor) is (x a), show by polynomial division that the other factor is (x + a).
c.x3 a3 is called a difference of cubes. Assuming one factor (the divisor) is (x a), find the other factor by polynomial division.
d.x4 a4 is called a difference of quartics. Assuming one factor (the divisor) is (x a), find the other factor by polynomial division.
e.Use polynomial division to factor a sum of cubes, x3 + a3. [Based on the above, make an assumption as to what one factor (the divisor) will be.]
f.Repeat part e) to factor a sum of squares, x2 + a2. What do you conclude?
3.Complete the following:
a.For the function f(x) = 3x2 - 5x + 11, find the slope of the secant to the curve in each of the given intervals:
i.x = 2 to x = 3
ii.x = 2 to x = 2.5
iii.x = 2 to x = 2.1
iv.x = 2 to x = 2.01
b.Extend this information to determine the slope of the tangent to the function in a), at x = 2.
4.Complete the following:
a.For the function g(x) = , find the slope of the secant to the curve in each of the given intervals:
i.x = 1 to x = 2
ii.x = 1 to x = 1.5
iii.x = 1 to x = 1.1
iv.x = 1 to x = 1.01
b.Extend this information to determine the slope of the tangent to the function in a), at x = 1.
5.Determine the equation of the polynomial function that matches each of the following data sets.
7.For the following graph:
Suzanne suggests that the parabolic shape of this graph indicates that this is most likely a quadratic function. Simon disagrees, as he believes that it must be a quartic function. Who is correct? Explain. (3 marks)
8.Graph each function given below on a graphing calculator to find a general rule for determining when a graph crosses the x-axis at an x-intercept or when the graph just touches and turns away from the x-axis. State the rule that you find.
a.y = (x + 1)2(x - 2)
b.y = (x - 4)3(x - 1)2
c.y = (x - 3)2(x + 4)4