Finding Zeros

FACTORING (Notes)

x^3+ 5x^2-4x-20
x^2(x-5)-4(x+5)
(x+5)(x^2-4)
(x+5)(x-2)(x+2)

Zeros for this Polynominal are: (-5,0)(2,0)(-2,0)

x^3+4x^2-9x-36
x^2(x+4)-9(x+4)
(x^2-9)(x+4)
(x-3)(x+3)(x+4)
Zeros for this Polynominals: (3,0)(-3,0)(-4,0)

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#1 LET y=x^2 & y^2 =x^4

2x^4 -x^2-3
2y^2-y-3
(2y-3)(y+1)
2y-3=0 or y+1=0
y=1.5 or y=1

x^2=1.5 or x^2=-1


#2

x^4-5x^2+4
y^2-5y+4
(y-4)(y-1)
y-4=0 or y-1=0
y=4 or y=1
x^2=4 or x^2=1
x=+/-2 or x=+/-1
(x+2)(x-2)(x+1)(x-1)

NOTES FOR 11-1-2010

BELL RINGER

Classify the following polynomials as

A.) Quadratic

B.) Cubic

C.) Quartic

D.) Quintic

1.) X^3-X^2+2

2.) X^5+6X^3-4

3.) X^2

4.) X^4-2X^2+2X

AGENDA

I. Bell Ringer

II. Solving Polynomialsusing synthetic substitution

Objective: Students will classify and solve polynomials

Big Picture: Data from science, business, and engineering can be modeled using polynomial curves

NOTES

Polynomials - one or more terms of an algebraic expression

Degree of a Polynomial- is defined by the largest exponent of the variable

EX.

3X^3 <------ Degree 3

3^3X <------ Degree 1

A polynomial with degree 3 can have at MOST 4 terms

Ax^3+Bx^2+Cx+D

Ax^3=first term

Bx^2=second term

Cx=third term

D=forth term

Synthetic Substitution- Is a method for solving any polynomial for a given value

P(X)= 3X^4-7X^3-5X^2+9X+10

P(2)=3(2)^4-7(2)^3-5(2)^2+9(2)+10

P(2)= 0

2_l 3 -7 -5 9 10

6 -2 -14 10

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3 -6 7 -5 20