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Solving Polynomial Equations by Factoring Factoring by grouping Ex. 1. Solve:

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Presentation on theme: "Solving Polynomial Equations by Factoring Factoring by grouping Ex. 1. Solve:"— Presentation transcript:

1 Solving Polynomial Equations by Factoring Factoring by grouping Ex. 1. Solve:

2 Variable substitution Another method of solving higher-degree polynomial equations involves recognizing polynomials that have quadratic form. Ex. 2. Solve

3 The Rational Root Theorem Let P(x) be a polynomial of degree n with integral coefficients and a nonzero constant term: If one of the roots of the equation P(x) = 0 is where P and q are nonzero integers with no common factor other than 1, then p must be a factor of and q must be a factor of

4 Ex. 3. a. According to the rational root theorem, what are the possible rational roots of is a possible rational root if p is a factor of –4 and q is a factor of 3.

5 b. Determine whether any of the possible rational roots really are roots. Then find all other roots, real or imaginary. Try synthetic substitution Or substitute in to see if any P(x) = 0 Use synthetic division

6 Find the other roots of Check x = -2 again because it may be a double root

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