4. Given the function f(x) = x5 + x4 - 9x³5x² + 16x + 12a. List all possible rational zeros of f.b. Given that x = -3 is a zero of f, fully factor f into a product of linear factors.c. Sketch the graph of y = f(x).-10-5-3 -2Y10864321-1-2-3-6-7-9-10-123810

Given function f(x)=x5+x4−9x3−5x2+16x+12

Answered: 4. Given the function f(x) = x5 + x4 −…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Determine whether the statement is true or false. If P(x) = (x-4)²(x+3)7, then the graph of the polynomial function y = P(x) crosses the x-axis at (4,0). Choose the correct answer below. ○ A. О в. ○ C. ○ D. The statement is false because (x-4)² is a factor of the given polynomial function P(x), and the exponent, 2 is even. Thus, the graph is tangent to the x-axis at (4,0). 2 The statement is true because (x-4)² is a factor of the given polynomial function P(x), and the exponent, 2 is even. Thus, the graph crosses the x-axis at (0,4). The statement is false because (x-4)² is a factor of the given polynomial function P(x), and the exponent, 2 is odd. Thus, the graph is tangent to the x-axis at (0,4). The statement is true because (x-4)² is a factor of the given polynomial function P(x), and the exponent, 2 is odd. Thus, the graph crosses the x-axis at (4,0).
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C. Choose the letter of the correct answer. 1. Which of the following is an example of polynomial function? A. f(x) =+ 3x-1 B. ffx) = 2a2x 2. From the choices, which polynomial function in factored form represents the glven graph? A. f(x) = (x+2) px+1) (x-1) B. f(x) = (x-2) (x+1) (x-1) C. fx) = xpx+2) (x+1) (x-1) D. fx) = x(x-2) (x+1) (x-1) C. f6) = V7s-2x D. Fx) = x*+ V3-S 3. If you will draw the graph of y=x (x+2)a, how will you sketch it with respect to the x-ads A. Sketch it crossing both (-2, 0) and (0. 0). B. Sketch it crossing (-2, 0) and tangent at (0. 0). C. Sketch it tangent at (-2, 0) and crossing (0, 0). D. Sketch it tangent at both (-2, 0) and (0. 0). 4. Your classmate Linus encounters difficulties in showing a sketch of the graph of y = 2x + 3x2 -4x -6. You know that the quickest technique is the leading coefficient test. You want to help Linus In his problem. What hint/clue should you give A. The graph fols to the left and rises to the right. B. The graph rises to both…
Write a polynomial that is best represented by the graph. (-7,0) (-6, 0) 10 | (1.0) y = x – 12x² + 29x + 42 y = x³ + 12x² + 29x – 42 O A) B.) y = x – 14x? + 55x – 42 y = x³ + 14x² + 55x + 42
Consider f (x) = 2x* – x3 – 5x2 + 2x + 2. 1. List all possible zeros (candidates) for f(x). 2. Define f (x) in your calculator or desmos. Use the graph to narrow down your candidates. Use synthetic division to reduce f (x) to a quadratic expression. Factor the resulting quadratic expression to find the last two zeros. ZEROS: 3. Express f(x) as a product of linear factors. Don't forget to include the value of a!
3. For the function f(x) = 2x4 – 5x3 + 9x² + x – 15: a. State the degree of the polynomial b. State the number of zeros the polynomial function will have. c. Use the Rational Zero Theorem to find all of the possible rational zeros d. Look at the graph or Table on a graphing calculator to determine which numbers on the list of rational zeros are real zeros indicated by the x-intercepts of the graph. In the space below, use synthetic division to verify one rational zero. Note: If the division remainder is zero, the number divided is a zero of the function. е. f. Find all remaining zeros. (Show work!) Note: Use the reduced polynomial (the quotient from the division) to continue the search for zeros © If the degree of the reduced polynomial is higher than 2, continue the synthetic division process with another real zero. (Remember: a number may be a multiple zero – i.e. occur more than once ) © Whenever the reduced polynomial is quadratic, the zeros can be found by using methods for…
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4. Given the function f(x) = x5 + x4 − 9x³ — 5x² + 16x + 12 a. List all possible rational zeros of f. b. Given that x = -3 is a zero of f, fully factor f into a product of linear factors. c. Sketch the graph of y = f(x). 10 9 8 7 6 5 4 -2 -3