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The Rational Zero Theorem states that, if the polynomial[latex]\,f\left(x\right)={a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+...+{a}_{1}x+{a}_{0}\,[/latex]has integer coefficients, then every rational zero of[latex]\,f\left(x\right)\,[/latex] has the form[latex]\,\frac{p}{q}\,[/latex]where[latex]\,p\,[/latex]is a factor of the constant term[latex]\,{a ...
The Factor Theorem now tells us \(\left(x-\frac{1}{3}\right)^2\) is a factor of \(p(x)\). Since \(x=3i\) is a zero and our final answer is to have integer (real) coefficients, \(x=-3i\) is also a zero. The Factor Theorem kicks in again to give us \((x-3i)\) and \((x+3i)\) as
The Rational Zero Theorem tells us that if [latex]\frac{p}{q}[/latex] is a zero of [latex]f\left(x\right)[/latex], then p is a factor of 1 and q is a factor of 2. [latex]\begin{cases}\frac{p}{q}=\frac{\text{factor of constant term}}{\text{factor of leading coefficient}}\hfill \\ \text{ }=\frac{\text{factor of 1}}{\text{factor of 2}}\hfill \end ...
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Precalculus Corequisite. Chapter 4: Polynomial and Rational Functions. Section 4.6: The Real Zeros of a Polynomial Function. Learning Outcomes. Evaluate a polynomial using the Remainder Theorem. Use the Factor Theorem to solve a polynomial equation. Use the Rational Zero Theorem to find rational zeros. Find zeros of a polynomial function.
MAT 206.5. Chapter 4: Polynomial and Rational Functions. Expand/collapse global location. Page ID. Table of contents. Evaluating a Polynomial Using the Remainder Theorem. Using the Rational Zero Theorem to Find Rational Zeros. Finding the Zeros of Polynomial Functions. Using the Fundamental Theorem of Algebra.
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Aug 16, 2023 · The Factor Theorem now tells us \(\left(x-\dfrac{1}{3}\right)^2\) is a factor of \(p(x)\). Since \(x=3i\) is a zero and our final answer is to have integer (real) coefficients, \(x=-3i\) is also a zero. The Factor Theorem kicks in again to give us \((x-3i)\) and \((x+3i)\) as factors of \(p(x)\).
