11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
March 15, 2012
SECTION 11-6&8:
FACTORING/SOLVING POLYNOMIALS
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*In some cases, we’ll have fewer zeros than the DEGREE à we'll have to alter!
G. Find the general form of a polynomial with zeros at ­1, 0, and 5, as a 4th degree.
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
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FIND THE FACTORS AND ROOTS
ROOTS : A solution to an equation (polynomial). The total possible # of roots is the same as the degree of the polynomial.
MULTIPLICITY OF A ROOT: the # of times a factor occurs
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
March 15, 2012
¶EXAMPLE PROBLEM:
*ROOTS:
*MULTPILICITY: In this example, we’d say…
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¶EXAMPLE PROBLEM:
*ROOTS:
*MULTPILICITY: In this example, we’d say…
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
March 15, 2012
¶QUADRATIC FORMULA
The QUADRATIC formula can tell us:
1) If there’re real or imaginary solutions by looking at the discriminant.
a) If Discriminant , real roots
b) If Discriminant <0, imaginary zeros
c) If Discriminant = Perfect square, polynomial will have whole number coefficients. 2) The solutions (roots) of the polynomial.
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b2 ­ 4ac is < 0!
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
March 15, 2012
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¶RECALL for 11.3 when we couldn't
factor a polynomial! Ex:
We can NOW solve for polynomials that
were prime, using imaginary numbers J
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
March 15, 2012
Factor
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Factor
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
March 15, 2012
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FACTORS:
ROOTS:
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
March 15, 2012
FACTORS:
ROOTS:
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FACTORS:
ROOTS:
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
March 15, 2012
FACTORS:
ROOTS:
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D. Consider
a.What is the total number of zeros?
b.Find the real zeros by using the graph.
c.What do we know about the remaining zeros?
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
March 15, 2012
E. Consider
a. What is the total number of zeros?
b. Name the real roots.
c. Name the imaginary roots.
d. Name the roots with their multiplicities.
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F. Find, name, and classify all of the roots.
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
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1. Find the roots by factoring.
Classify the roots as real or imaginary,
and give their multiplicities.
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2. Consider the equation
a .How many roots are there?
b. Find and classify the roots as real or
imaginary, and give their multiplicities.
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11.6 and 11.8 Factoring Quadratics and Solving Polynomial Equations.notebook
March 15, 2012
3. Find the roots of
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4. Does this polynomial
have real or imaginary zeros
(hint…find the discriminant)?
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