Solving Polynomial and Rational Equations
Master key strategies and concepts for solving polynomial and rational equations and inequalities.
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Questions Covered in This Set
8 cards to master
What is the Zero Product Property?
If ab = 0, then a = 0 or b = 0. This property allows us to solve factored polynomial equations by setting each factor equal to zero.
What are the five steps for solving polynomial equations?
1) Move everything to one side (set equal to zero), 2) Factor completely, 3) Apply Zero Product Property, 4) Solve resulting equations, 5) Check for extraneous solutions.
What is the first critical step when solving rational equations?
Identify restrictions by determining values that make any denominator zero. These values cannot be solutions.
How do you clear fractions in a rational equation?
Multiply every term by the least common denominator (LCD) of all fractions in the equation.
What is the sign chart method used for?
The sign chart method is used to solve polynomial and rational inequalities by testing the sign of the expression in intervals between critical points to find which intervals satisfy the inequality.
What are critical points in the context of rational inequalities?
Critical points are the zeros of the numerator and the zeros of the denominator. They divide the number line into intervals to test.
Why must you always check solutions in rational equations?
To reject any solutions that make a denominator zero (violate restrictions). These are extraneous solutions that must be excluded.
When solving inequalities, why shouldn't you multiply by a variable expression?
The variable expression might be negative in some intervals, which would flip the inequality sign. Use the sign chart method instead.
