# Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. f(x) = 2x^{3} + 8x^{2 }+ 7x - 8

**Solution:**

We can use the rational zero theorem to find rational zeros of a polynomial.

By Rational Zero Theorem,

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)

q is a factor of the leading coefficient of P(x)

Possible value of rational zero is p/q

Given, f(x) = 2x^{3} + 8x^{2 }+ 7x - 8

Here, constant term, p = -8

Leading coefficient, q = +2

The factors of the constant term -8 are ±1, ±2, ±4, ±8.

The factor of the leading coefficient is ±1 and ±2.

Possible values of rational zeros p/q = ±1/±1, ±2/±1, ±4/±1, ±8/±1, ±1/±2, ±4/±2, ±8/±2.

Therefore, the values of possible rational zeros are ±1, ±2, ±4, ±8.

## Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. f(x) = 2x^{3} +8x^{2}+7x-8

**Summary:**

Using the rational zeros theorem, all possible rational zeros of the function f(x) = 2x^{3} + 8x^{2} + 7x - 8 are ±1, ±2, ±4, ±8.

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