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Find rational zeros of f(x) = 2 x 3 + 3 x 2 – 8 x + 3 by using synthetic division. Each line in the table that follows represents the “quotient line” of the synthetic division. p/q 2 3 –8 3 | 1 | 2 | 5 | –3 | 0 | 1 is a zero. | –1 | 2 | 1 | –9 | 12 | | | 2 | 4 | –6 | 0 | is a zero. | | 2 | 2 | –9 | | | 3 | 2 | 9 | 19 | 60 |
The Rational Zeros Theorem states: If P ( x ) is a polynomial with integer coefficients and if is a zero of P ( x ) ( P ( ) = 0 ), then p is a factor of the constant term of P ( x ) and q is a factor of the leading coefficient of P ( x ) .
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 ...
Rational Zero Theorem Statement. The rational zero theorem states that each rational zero(s) of a polynomial with integer coefficients f(x) = \(a_{n}x^{n}+a_{n-1}x^{n-1}+.....+a_{2}x^2+a_{1}x+a_{0}\) is of the form p/q, where. p is a factor of the constant \(a_0\) and; q is a factor of the leading coefficient \(a_n\).
The Rational Zeros Theorem is a helpful tool in polynomial algebra, assisting in determining potential rational zeros of a polynomial. How to Use the Rational Zeros Theorem? The Rational Zeros Theorem provides a method to determine all possible rational zeros (or roots) of a polynomial function.
In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational solutions of a polynomial equation a n x n + a n − 1 x n − 1 + ⋯ + a 0 = 0 {\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{0}=0}
13 de feb. de 2018 · 7.73M subscribers. 19K. 1.4M views 6 years ago New Precalculus Video Playlist. This precalculus video tutorial provides a basic introduction into the rational zero theorem. It explains how to...
