Problem

Use the rational zeros theorem to list all possible zeros of the function $f(x)=7 x^{3}-3 x^{2}-x+2$ Enter the possible zeros separated by commas. You do not need to factor the polynomial.

Solution

Step 1 :Given the function \(f(x)=7 x^{3}-3 x^{2}-x+2\).

Step 2 :We use the Rational Root Theorem which states that if a polynomial has a rational root, then it must be a factor of the constant term divided by a factor of the leading coefficient.

Step 3 :In this case, the constant term is 2 and the leading coefficient is 7.

Step 4 :The factors of 2 are 1 and 2, and the factors of 7 are 1 and 7.

Step 5 :Therefore, the possible rational roots are \(\pm1, \pm2, \pm\frac{1}{7}, \pm\frac{2}{7}\).

Step 6 :\(\boxed{\text{The possible rational zeros of the function } f(x)=7 x^{3}-3 x^{2}-x+2 \text{ are } \pm1, \pm2, \pm\frac{1}{7}, \pm\frac{2}{7}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8675/

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