Rational Root Theorem

What this lesson shows

You need a root of a polynomial and there is no formula to hand. Guessing at random could take all day. The Rational Root Theorem tells you the only guesses worth making.

Try it yourself

Real questions from this lesson's worksheets — answers below each one.

1. For x² − x − 6 (leading coefficient 1), the possible rational roots are ± the divisors of which number?
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   6
2. By the Rational Root Theorem, which of these is a POSSIBLE rational root of x² − x − 6? (leading coefficient 1)
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   2
3. Use the Remainder Theorem to find the remainder when x² + 2x + 1 is divided by (x − 1).
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   4
4. How many POSITIVE divisors does 6 have? (the count of possible positive rational roots of x² − x − 6)
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   4