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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
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
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
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
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