Algebra II Question?

Question

Let f(x) = 5x - 26 and g(x) = 6x.

Part 1 [4 points] What is (f ◦ g)(x) ?
Part 2 [2 points] Use complete sentences to describe the method you used to solve this problem.

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10. Graph the function f(x) = –x^3 + 2

Part 1 [3 points] Use complete sentences to explain the process of graphing f(x) = –x^3 + 2 .
Part 2 [3 points] What is the end behavior of f(x) = –x^3 + 2 ?

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11. The binomial x + 4 is one factor of 3x^3 + 5x^2 – 26x + 8. Use complete sentences to explain how you use (either) polynomial division or synthetic division to find the remaining factors. List the remaining factors.

Answer 1

10) Let y = -x³ + 2.

To plot the graph we need some points.

So take some values for x in-order to find y.

x	y = -x3 + 2	(x,y )
-1	y = -(-1)3 + 2 = 3	(-1,3)
0	y = -(0)3 + 2 = 2	(0,2)
1	y = -(1)3 + 2 = 1	(1,1)

Plot the points in the graph and join them.

The end behavior of the function is negative cubic.

Answer 2

11) The polynomial 3x³ + 5x²  – 26x + 8.

Factor or divisor is x + 4

x + 4 = 0

Sbtract 4 from each side.

x + 4 - 4 = 0 - 4

x = -4

By synthetic division        

The expression obtained is 3x²  - 7x + 2.

3x²  - 7x + 2

3x²  - 6x - x + 2

3x(x  - 2) - 1(x - 2)

(3x  - 1) (x - 2)

Remaining factors are (3x  - 1) and (x - 2).