Use the Rational Zero Theorem to list all possible rational zeros for the function f(x) = x^3 + x^2 - 4x - 4.

Question
Rational functions
asked 2020-11-08
Use the Rational Zero Theorem to list all possible rational zeros for the function \(f(x) = x^3 + x^2 - 4x - 4\).

Answers (1)

2020-11-09
possible rational \(zeros=(Factors of the constant term)/(Factors of the leading coefficient)\)
List the factors of the constant term and the leading coefficient of the given function.
Factors of the constant term, -4: +-1, +-2, +-4
Factors of leading co efficient, 1: +-1
possible rational \(zeros=(Factors of -4)/(Factors of 1)\)
\(=(+-1,+-2,+-4)/(+-1)\)
consider each number is numerator an divide it by each number in the denominator.
Possible rational zeros= +-1, +-2, +-4
Therefore, the possible rational seros of f(x) are
+-1, +-2 and +-4
0

Relevant Questions

asked 2020-10-20
The function \(\displaystyle{f{{\left({x}\right)}}}={x}\frac{{\left({64}-{x}^{{2}}\right)}^{{1}}}{{2}}\) satisfies the hypotheses of Rolle's Theorem on the interval [-8,8]. Find all values of that satisfy the conclusion of the theorem.
a.) + 1, AND -1
b.) \(\displaystyle+{4}\sqrt{{{2}}}{\quad\text{and}\quad}-{4}\sqrt{{{2}}}\)
c.) \(\displaystyle{4}\sqrt{{{2}}}\)
d.) 1
My answer. The intervals do match and equal zero so Rolles theorem can work.
Second I found the derivative maybe thats where I can't solve this problem.
The derivative that I got was \(\displaystyle{64}-{x}^{{2}}+\frac{{x}}{\sqrt{{{64}-{x}^{{2}}}}}\) maybe i did wrong on the simplifying. I at least tried hopefully some one can explain as much as possible with every single step because I can figure out the algebra part.
asked 2021-02-21
Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
Find the real zeros of \(f(x) = 5x^{3}\ -\ x^{2}\ +\ 5x\ -\ 1\)
asked 2020-12-06
For each polynomial function, one zero is given. Find all rational zeros and factor the polynomial. Then graph the function. f(x)=3x^{3}+x^{2}-10x-8ZSK, zero:2
asked 2020-11-03
Find Infinite limit (Rational Function)
underset \((x->5^+)(lim)(1/x^(4/3)-1/(x-5)^(4/3))\)
asked 2020-11-05
Identify each of the following functions as polynomial, rational, algebraic, or transcendental
\(f(x)=(2x^3+3x)/(9-7x^2)\)
asked 2021-03-06
Construct a rational function whose domain is all real numbers. Provide evidence as to why the domain of your rational function is all real numbers.
asked 2021-02-21
Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. Zeros: -1, multiplicity 1, 3, multiplicity 2, degree 3
asked 2021-02-11
Construct a rational function that has a vertical asymptote at \(x = 3\) and a removable discontinuity at \(x = -2\).
Explain how you determined your answer.
asked 2021-01-31
True or False. The domain of every rational function is the set of all real numbers.
asked 2020-11-05
Given that Domain of the rational function is all real numbers.
So the rational function should not contain denominator part.
...