Rational Zero Theorem (Jump to: Lecture | Video )

Rational Zero Theorem

If a polynomial equation has integer coefficients, then any rational zero must be in the form of

where p is a factor of the constant term, and q is a factor of the leading coefficient.

Find the rational zeros of:

Figure 1.

First, we determine the factors of the leading coefficient and the constant:

Figure 2.

Next, we perform synthetic division using each p/q term is the divisor. Any row that has no remainder is a 0 for this function.

Figure 3.

The value of the function is 0 when x = -3, x = 1/2, and x = 1.

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