Mary Jane Sterling - Algebra I - 1001 Practice Problems For Dummies (+ Free Online Practice)

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642–645 Solve each quadratic equation by “completing the square.”

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646–653 Rewrite each as a complex number in the form .

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654–655 Use the quadratic formula to solve the equations. Write your answers as complex numbers.

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Chapter 15

Apolynomial is a smooth curve that goes on and on forever, using input variables going from negative infinity to positive infinity. To solve a polynomial means to set the equation equal to 0 and determine which, if any, numbers create a true statement. Any numbers satisfying this equation give you important information: They tell you where the graph of the polynomial crosses or touches the x- axis.

Solving polynomials in this chapter requires the following techniques:

Counting the number of possible real roots/zeros, using Descartes’s Rule of Signs

Making a list of the possible rational roots/zeros, using the Rational Root Theorem

Putting Descartes’s Rule of Signs and the Rational Root Theorem together to find roots

Applying the Factor Theorem

Solving polynomial equations by factoring

Applying synthetic division

As you probably know, you can come up with a different answer to a math problem by simply confusing or forgetting one step; here are some things to watch out for:

Confusing real roots with rational roots; rational roots are real, but real roots aren’t necessarily rational

Being sure to list all the possible divisors of a number, not missing multiples

Remembering to change the sign of the numerical part of the divisor when using synthetic division

Taking roots with multiplicity of more than one into account when looking for factors

656–659 Count the possible number of positive and negative real roots of the equation.

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660–663 List all the possible rational roots for each polynomial equation.

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