Section 6-2: Polynomials and Linear Factors

Goal 1.03: Operate with algebraic expressions (polynomial, rational,

complex fractions) to solve problems.

Standard Form vs Factored Form

f(x) = x3 – 2x2 – 8x f(x) = x(x – 4)(x + 2) In factored form you can easily

determine the zeros of the function (zeros = x-intercepts)

Finding zeros and multiplicity of functions in factored form:

1. y= x(x + 8)(x – 2)x= 0, x= -8, x= 2 all multiplicity of 1

2. y= x(x – 8)2

x= 0, x= 8 with a multiplicity of 23. y= x2(x + 4)(x – 3)

x= 0 with multiplicity of 2, x= -4, x= 34. y= (x2 – 4 )(x2 – 9)

x= -2, x= 2, x= -3, x= 3 5. y= (x – 2)(x + 7)3

x= -7 with a multiplicity of 3, x = 2

Write a Polynomial Function in Standard Form with the given zeros:

1. –1, 0, 2x(x + 1)(x – 2)(x2 + x)(x – 2)x3 – 2x2 + x2 – 2xx3 – x2 – 2x

2. –1, 3, 4(x + 1)(x – 3)(x – 4)(x + 1)(x2 – 4x – 3x + 12)(x + 1)(x2 – 7x + 12)x3– 7x2 + 12x + x2 – 7x + 12x3 – 6x2 + 5x + 12

3. –2 with a multiplicity of 3(x + 2)3

(x + 2)(x + 2)(x + 2)

Write each Polynomial in factored form

1. x3 – 7x2 + 10xx(x2 – 7x + 10)x(x – 5)(x – 2)

2. x3 – 6x2 – 16x

3. x3 + 7x2 + 12x 4. x3 – 8x2 + 15x

Finding the relative extrema and zeros of the function by graphing:

f(x) = x3 – x2 – 9x + 9

Classwork/Homework

• Classwork: • P. 311 #3, 11, 15, 19, 23, 29

• Homework: • P. 311 #4, 8, 14, 18, 22, 34