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Solving equationsSolving polynomial equations by factoring:Solve: 3X 3X 3X 3X 3X X = 0 X = 4 X = -4 Solve for X. Solve: X (X (X - 1)(X + 1)(X X - 1 = 0 X + 1 = 0 X X = 1 X = -1 X
Solve: X X(X X(X + 1)(X - 3) = 0 Factor completely. X = 0 X + 1 = 0 X - 3 = 0 Set each factor equal to zero. X = 0 X = -1 X = 3 Solve for X. Solving equations involving rational exponents:The first step is to isolate the rational expression. Second, determine the rational exponent and raise both sides of the equation to the reciprocal exponent. Simplify and check your answers. Example: 4X 4X X (X X = 2
Check: 4X 4(2 4(2) - 8 = 0 Simplify 8 - 8 = 0 0 = 0 The statement is true; therefore, the solution checks. Solving Radical Equations:The basic approach to solving radical equations is to get rid of the radical equation. Get rid of the square root by squaring each side of the equation. Get rid of the cube root by cubing each side of the equation, etc.. When changing radical equations and those equations involving rational exponents we often get extraneous solutions (solutions that do not fit the original equation). Therefore, a check of each tentative solution is required. Example:
Solving Equations involving fractions:To solve an equation involving fractions, multiply both sides of the equation by the least common denominator of each term in the equation. This procedure will clear the equation of fractions. Solve the following equations that contain fractions and check the tentative solutions: Example:
Solving equations involving absolute values:To solve an equation involving an absolute value, consider the fact that the expression inside the absolute value can be positive or negative. This consideration results in two separate equations, each of which must be solved. Example:
Both x = 5 and x = -1 are solutions.
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