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Mar 3, 2023 · 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
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 \(p(x)\).
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 ...
Use the Rational Zero Theorem to find rational zeros. Find zeros of a polynomial function. Use Descartes’ Rule of Signs. Solve real-world applications of polynomial equations. A new bakery offers decorated sheet cakes for children’s birthday parties and other special occasions. The bakery wants the volume of a small cake to be 351 cubic inches.
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Use the Rational Zero Theorem to find rational zeros. Find zeros of a polynomial function. Use the Linear Factorization Theorem to find polynomials with given zeros. Use Descartes’ Rule of Signs. Solve real-world applications of polynomial equations.
Use the Rational Zero Theorem to find rational zeros. Find zeros of a polynomial function. Use the Linear Factorization Theorem to find polynomials with given zeros.
The Fundamental Theorem of Algebra tells us that every polynomial function has at least one complex zero. This theorem forms the foundation for solving polynomial equations. Suppose f is a polynomial function of degree four, and f (x) = 0 f ( x) = 0.
