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37. Degree 3; x = 1 is a zero of multiplicity 2 and the origin is the y-intercept.

37. Degree 3; x = 1 is a zero of multiplicity 2 and the origin is the y-intercept.

Algebra and Trigonometry (6th Edition)
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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Question

number 37

The text refers to polynomial functions and their properties. Below is the transcription suitable for an educational website: --- ### Polynomial Functions Exercises #### Polynomial Equations **29.** \( p(x) = x^4 + 4x^3 - x^2 + 16x - 20 \) **30.** \( p(x) = x^4 - 6x^3 + 9x^2 - 24x + 20 \) **31.** \( p(x) = 2x^4 + 9x^3 - 7x^2 - 9x + 5 \) **32.** \( p(x) = 2x^4 + 7x^3 + x^2 - 7x - 3 \) **33.** \( p(x) = 2x^4 - 5x^3 + 8x^2 - 15x + 6 \) **34.** \( p(x) = 2x^4 - x^3 + 5x^2 - 3x - 3 \) --- #### Exercise Instructions **In Exercises 35–40, find an expression for a polynomial \( p(x) \) with real coefficients satisfying the given conditions. There may be more than one possible answer.** **35.** Degree 2; \( x = 2 \) and \( x = -1 \) are zeros. **36.** Degree 2; \( x = \frac{1}{2} \) and \( x = \frac{3}{4} \) are zeros. **37.** Degree 3; \( x = 1 \) is a zero of multiplicity 2 and the origin is the \( y \)-intercept. **38.** Degree 3; \( x = -2 \) is a zero of multiplicity 2 and the origin is an \( x \)-intercept. **39.** Degree 4; \( x = 1 \) and \( x = \frac{1}{3} \) are both zeros of multiplicity 2. **40.** Degree 4; \( x = -1 \) and \( x = -3 \) are zeros of multiplicity 1 and \( x = \frac{1}{3} \) is a zero of multiplicity 2. --- These exercises are designed
Transcribed Image Text:The text refers to polynomial functions and their properties. Below is the transcription suitable for an educational website: --- ### Polynomial Functions Exercises #### Polynomial Equations **29.** \( p(x) = x^4 + 4x^3 - x^2 + 16x - 20 \) **30.** \( p(x) = x^4 - 6x^3 + 9x^2 - 24x + 20 \) **31.** \( p(x) = 2x^4 + 9x^3 - 7x^2 - 9x + 5 \) **32.** \( p(x) = 2x^4 + 7x^3 + x^2 - 7x - 3 \) **33.** \( p(x) = 2x^4 - 5x^3 + 8x^2 - 15x + 6 \) **34.** \( p(x) = 2x^4 - x^3 + 5x^2 - 3x - 3 \) --- #### Exercise Instructions **In Exercises 35–40, find an expression for a polynomial \( p(x) \) with real coefficients satisfying the given conditions. There may be more than one possible answer.** **35.** Degree 2; \( x = 2 \) and \( x = -1 \) are zeros. **36.** Degree 2; \( x = \frac{1}{2} \) and \( x = \frac{3}{4} \) are zeros. **37.** Degree 3; \( x = 1 \) is a zero of multiplicity 2 and the origin is the \( y \)-intercept. **38.** Degree 3; \( x = -2 \) is a zero of multiplicity 2 and the origin is an \( x \)-intercept. **39.** Degree 4; \( x = 1 \) and \( x = \frac{1}{3} \) are both zeros of multiplicity 2. **40.** Degree 4; \( x = -1 \) and \( x = -3 \) are zeros of multiplicity 1 and \( x = \frac{1}{3} \) is a zero of multiplicity 2. --- These exercises are designed
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