Please show work and explain 3. Consider the functionf(x) = 7x³ + 5x² + 12x – 4.Use the Rational Zeros Test to do thefollowing.2is a zero of f, find all zeros of7A. If k =f.B. Write f(x) in factored form.

Answered: Consider the function 7x + 5x² + 12x –…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter5: Polynomial And Rational Functions

Section: Chapter Questions

Problem 14PT: Use the Rational Zero Theorem to help you find the zeros of the polynomial functions. 14....

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Please show work and explain

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:

$\begin{array}{l} f (x) = 7 x^{3} + 5 x^{2} + 12 x - 4 \\ According to the Rational Roots Test: \\ Find the constant term and leading cooeffient of f (x), \\ Constant term, a_{0} = - 4 \\ Leading cooeffient, a_{n} = 7 \\ The every rational root of f (x) is of the form: \\ \frac{p}{q} = \frac{\pm (Factors of a_{0})}{\pm (Factors of a_{n})} \\ Factors of a_{0} = 1, 2, 4 \\ Factors of a_{n} = 1, 7 \\ \frac{p}{q} = \frac{\pm (1, 2, 4)}{\pm (1, 7)} \\ = \pm 1, \pm 2, \pm \frac{2}{7}, \pm 4, \pm \frac{4}{7} \\ = - 1, 1, - 2, 2, - \frac{2}{7}, \frac{2}{7}, - 4, 4, - \frac{4}{7}, \frac{4}{7} \end{array}$

Step 2

Verify the polynomials:

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