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Section 1.6 SolvingEquations

# It is frequently dicult to factor a polynomial of

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Unformatted text preview: t is frequently diﬃcult to factor a polynomial of degree greater than 2. Outline Solving Polynomial Equations Solving Rational Equations Rational Exponents Examples Example Solve the following polynomial equations. x 3 = 13x 2 − 42x . x 4 − 81 = 0. x 6 − 2x 4 − x 2 + 2 = 0. Hint: Factor by grouping. Applications Outline Solving Polynomial Equations Solving Rational Equations Rational Exponents Applications Rational Equations Deﬁnition A rational equation is an equation that can be written in the form an x n + an−1 x n−1 + · · · + a2 x 2 + a1 x + a0 =0 bm x m + bm−1 x m−1 + · · · + b2 x m + b1 x + b0 where n, m are nonnegative integers, a0 , a1 , a2 , . . . , an−1 , an and b0 , b1 , b2 , . . . , bn−1 , bn are real number constants. To solve a rational equation, we factor, simplify, then use the zero product property to ﬁnd the solutions of the equation in the numerator. Check your answers! It is possible to get extraneous solutions (values that are not true solutions). Outline Solving Polynomial Equations Solving Rational Equations Examples Example Solve th...
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