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HelloKitty17
 one year ago
A function is shown below:
f(x) = x3 + 3x2  x  3
Part A: What are the factors of f(x)? Show your work. (3 points)
Part B: What are the zeros of f(x)? Show your work. (2 points)
Part C: What are the steps you would follow to graph f(x)? Describe the end behavior of the graph of f(x). (5 points)
HelloKitty17
 one year ago
A function is shown below: f(x) = x3 + 3x2  x  3 Part A: What are the factors of f(x)? Show your work. (3 points) Part B: What are the zeros of f(x)? Show your work. (2 points) Part C: What are the steps you would follow to graph f(x)? Describe the end behavior of the graph of f(x). (5 points)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Use factoring by grouping.

OregonDuck
 one year ago
Best ResponseYou've already chosen the best response.1A) (x + 4)( ) = x^3 + 4x^2 – x – 4 I know the first term must be x^2, since x^3/x = x^2: (x + 4)(x^2 ) = x^3 + 4x^2 – x – 4 I know the second term must be 0, since 4x ^2  (4 * x^2) = 4x^2  4x^2 = 0: (x + 4)(x^2 + 0 + ) = x^3 + 4x^2 – x – 4 I know the last term must be 1, since x  (0 * x) = x  0x = x: (x + 4)(x^2  1) Now, factor the second part. It's a difference of squares, so: f(x) = (x + 4)(x + 1)(x  1)<=====ANSWER B) Set each factor = to 0: x + 4 = 0; x + 1 = 0; x  1 = 0 x = 4. 1. and 1<=====ANSWER C) Plot the 0's. Solve the equation for numbers that are less than 4, between 4 and 1, between 1 and 1, and greater than 1. I chose 5, 2, 0 and 2: f(5) = (5 + 4)(5 + 1)(5  1) = (1)(4)(6) = 24 f(2) = (2 + 4)(2 + 1)(2  1) = (2)(1)(3) = 6 f(0) = 0^3 + 4(0)^2  0  4 = 4 f(2) = (2 + 4)(2 + 1)(2  1) = 18 The end behavior means which way do the ends of the graph point. On the left side, it points down, so it's negative; on the right side, it points up, so it's positive.
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