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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

8. Polynomial Models in the Real World

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Exercise 40 Page 338

We say that b is a zero of multiplicity n when (x-b) appears n times as a factor of a polynomial.

Zero of Multiplicity 2: 1/4

Practice makes perfect

We want to determine the zeros of the given polynomial function as well as their multiplicity. We say that b is a zero of multiplicity n when (x- b) appears n times as a factor of a polynomial. Let's factor the given function in order to find the zeros.

y=16x^2-8x+1

FacNegPerfectSquare

a^2-2ab+b^2=(a-b)^2

y=(4x-1)^2

Factor out 4

y=(4(x-1/4))^2

(a * b)^m=a^m* b^m

y=4^2(x-1/4)^2

Calculate power

y=16(x-1/4)^2

Let's now use a table to organize the information. Note that, since 16≠ 0, it cannot be a zero.

Factor	Appearances	Zero	Multiplicity
x- 1/4	2	1/4	2

We can say that 14 is a zero of multiplicity 2.

Subchapter links

Lesson Check p.335

Practice and Problem-Solving Exercises p.335-337

Standardized Test Prep p.338

Mixed Review p.338