5.3 Solving Polynomial Equations

Real Vs. ImaginaryIn Chapter 4, we found both real

and imaginary solutions for quadratic equations.

We can find both real and imaginary solutions for polynomial equations too!◦Remember:

To Solve a Polynomial Equation by Factoring:1. Set the equation = 02. Factor (Remember GCF first!)3. Apply the Zero-Product Property

(Set each factor = 0 and solve for x)

If you have a quadratic that is not factorable, use the quadratic formula

Example: Find the real or imaginary solutions of each equation.

Example: Find the real or imaginary solutions of each equation.

Factoring a Sum or Difference of CubesTo factor a sum or difference of

cubes, we use the following “shortcut”

Example: Factor

Factoring by SubstitutionFactoring by substitution is useful

when you have a polynomial of degree 4 or higher and no GCF

It is also useful if you have a variable in the denominator (more about this later!)

Solving by Factoring with Substitution1. Write the polynomial in standard

form2. Identify the piece that will be

substituted3. Substitute4. Factor5. Undo the substitution6. Solve for the variable

Find the real or imaginary solutions of each equation by factoring.

Find the real or imaginary solutions of each equation by factoring.

Finding Real Roots by Graphing1. Write the equation in standard

form2. Enter the equation into3. Use the zero feature to find all

real zeros

Example: Find the Real Solutions of the equation by graphing.

AssignmentClasswork: p 301 #25 – 29 odd

Homework: p 301 #11 – 23odd, 39 – 49odd, not 45