PreCalculus Section 2.6 Solve polynomial equations by factoring and the Rational Roots Theorem. Solve by factoring: x 3 + 5x 2 – 4x – 20 = 0 x 6 – x 3.

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Presentation transcript:

PreCalculus Section 2.6 Solve polynomial equations by factoring and the Rational Roots Theorem. Solve by factoring: x 3 + 5x 2 – 4x – 20 = 0 x 6 – x 3 – 6 = 0

What are the possible roots of P(x) = 3x 3 + 8x 2 - 9x + 2 ? What are the actual roots of P(x)? Rational Roots Theorem Let P(x) be a polynomial function of degree n with integral coefficients and a nonzero constant term: P(x) = ax n + bx n-1 + cx n-2 + …dx + e If p/q is a root of P(x) then p is factor of “e” and “q” is a factor of “a”.

Solve 3x x x 2 – 4 = 0 2x 4 + 3x 3 - 7x 2 – 12x – 4 = 0 Assign: page 83 Problems 2-24 even, 15, 19, 25