Consider the function 7x + 5x² + 12x – 4. f(x) = Use the Rational Zeros Test to do the following. A. If k = is a zero of f, find all zeros of 7 f. B. Write f(x) in factored form.

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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3. Consider the function
f(x) = 7x³ + 5x² + 12x – 4.
Use the Rational Zeros Test to do the
following.
2
is a zero of f, find all zeros of
7
A. If k =
f.
B. Write f(x) in factored form.
Transcribed Image Text:3. Consider the function f(x) = 7x³ + 5x² + 12x – 4. Use the Rational Zeros Test to do the following. 2 is a zero of f, find all zeros of 7 A. If k = f. B. Write f(x) in factored form.
Expert Solution
Step 1

Consider the given:

fx=7x3+5x2+12x4According to the Rational Roots Test:Find the constant term and leading cooeffient of fx,Constant term,a0=4Leading cooeffient,an=7The every rational root of fx is of the form:pq=±Factors of a0±Factors of anFactors of a0=1,2,4Factors of an=1,7pq=±1,2,4±1,7   =±1,±2,±27,±4,±47   =1,1,2,2,27,27,4,4,47,47

Step 2

Verify the polynomials:

Algebra homework question answer, step 2, image 1

 

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