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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![**Task: Write a polynomial function, P, in factored form by using the given information.**
Given:
- Polynomial \( P \) is of degree 3.
- \( P(0) = 12 \).
- Zeros of the polynomial: \(-6, 1, -2\).
To write the polynomial in factored form, use the zeros to express \( P(x) \) as:
\[ P(x) = a(x + 6)(x - 1)(x + 2) \]
To find the leading coefficient \( a \), use the given information that \( P(0) = 12 \):
Substitute \( x = 0 \) into the equation:
\[ P(0) = a(0 + 6)(0 - 1)(0 + 2) = a \cdot 6 \cdot (-1) \cdot 2 = a \cdot (-12) \]
Since \( P(0) = 12 \), we have:
\[ a \cdot (-12) = 12 \]
Solving for \( a \):
\[ a = -1 \]
Therefore, the polynomial in factored form is:
\[ P(x) = -(x + 6)(x - 1)(x + 2) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fe4e0d9-a441-4076-9243-8e98c4a90bfe%2F6fa3e28f-a874-444c-b326-2480d2d831bd%2Fcet5o6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Task: Write a polynomial function, P, in factored form by using the given information.**
Given:
- Polynomial \( P \) is of degree 3.
- \( P(0) = 12 \).
- Zeros of the polynomial: \(-6, 1, -2\).
To write the polynomial in factored form, use the zeros to express \( P(x) \) as:
\[ P(x) = a(x + 6)(x - 1)(x + 2) \]
To find the leading coefficient \( a \), use the given information that \( P(0) = 12 \):
Substitute \( x = 0 \) into the equation:
\[ P(0) = a(0 + 6)(0 - 1)(0 + 2) = a \cdot 6 \cdot (-1) \cdot 2 = a \cdot (-12) \]
Since \( P(0) = 12 \), we have:
\[ a \cdot (-12) = 12 \]
Solving for \( a \):
\[ a = -1 \]
Therefore, the polynomial in factored form is:
\[ P(x) = -(x + 6)(x - 1)(x + 2) \]
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