Polynomial f(x) Review

Presentation

•

Mathematics

•

10th - 12th Grade

•

Easy

•

CCSS

HSA.APR.B.3, HSF-IF.C.7C, HSA.APR.B.2

Standards-aligned

John Phillips

Used 1+ times

FREE Resource

7 Slides • 22 Questions

Polynomial f(x) Review

Reviewing Polynomial Functions, Roots, Division, and Graphical Behavior

Necessary Skills

The Factor Theorem: Understanding that if f(a) = 0, then (x - a) is a factor of the polynomial function f(x)
The Remainder Theorem: When using division with a particular divisor, if the remainder is 0, then the divisor is a factor of the dividend polynomial function p(x)
End Behavior: Based on degree (highest exponent) as well as leading coefficient (positive or negative)

Multiple Choice

Even or Odd degree?

even

odd

Multiple Choice

What degree is the function?

Multiple Choice

Which function is graphed?

(x - 4)(x + 2)(x - 8)=y

(x - 4)(x - 2)(x + 8)=y

(x - 4)(x + 2)(x + 8)=y

(x + 4)(x + 2)(x + 8)=y

Multiple Choice

Is the leading coefficient positive or negative

positive

negative

Multiple Choice

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

-2, 3 (multiplicity 2), 4

-2 (multiplicity 2), 3, 4

2, -3 (multiplicity 2), -4

2 (multiplicity 2), -3, -4

Multiple Choice

What is the degree of the function graphed here?

Multiple Choice

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

f(x) = (x-4)(x-1)²(x+2)(x+4)

f(x) = (x-4)(x+1)²(x+2)(x+4)

f(x) = (x+4)(x+1)(x-2)(x+4)

f(x) = (x+4)(x+1)²(x-2)(x-4)

Multiple Choice

If a zero of a polynomial function has multiplicity 4 that means:

The x intercept is at (4, 0)

The graph will "bounce back" at that zero

The graph will "pass through" at that zero

Zeros cannot have multiplicity of 4

Multiple Choice

Write a 4th degree polynomial function with:
*a positive leading coefficient
*zeros: 9, 3, -2, 0

y = x(x - 9)(x - 3)(x + 2)

y = x(x + 9)(x + 3)(x - 2)

y = -x(x - 9)(x - 3)(x + 2)

y = -x(x + 9)(x + 3)(x - 2)

Multiple Choice

y = ^_(x + 2)(x - 1)²

y = -(x - 2)(x + 1)²

y = (x - 2)(x + 1)²

y = -x³

How do we use Division?

When given a polynomial p(x), we may also be given a potential factor (x - a). We divide by (x - a) to determine if it is a factor...if the remainder = 0, success.
We can then analyze the quotient to see if it is factorable and will reveal additional factors and eventually roots/zeros of the function p(x)

Multiple Choice

Find the zeros of the polynomial given one factor.

X= 3,4,5

x=-3,-4,-5

x=-3,4,5

x= 3, -4, -5

Multiple Choice

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

f(x) = (x+2)(x-1)(x-4)

f(x) =x³ - 3x² - 6x + 8

f(x) = x³+ 8

f(x) = x³ - 3x² + 8

Multiple Choice

How could you determine if x-2 is a factor of 2x³-5x²+x-2?

Use synthetic division and see if the quotient is even

Ask the person sitting next to me

Use synthetic division and see if the remainder is zero

Flip a coin

Multiple Choice

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

Degree: 6

Degree: 5

Degree: 3

Degree: 2

Multiple Choice

Is (x-4) a factor of (x³ +x² -16x-16)?

YES

Multiple Choice

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

-4, -1, 3

3, -3, 4, 1

4, 1, -3

3, -4, -1, 3

Multiple Choice

Multiply the following together:

(2x + 3)(x² + 4x + 1)

2x³ + 8x²+2x

3x² + 12x +3

2x³ +11x² +14x +3

2x³ + 12x +3

Multiple Choice

Factor this expression:

2x³ + 2x² - 24x

(Hint: GCF and Slide-n-Divide)

2x(x + 4)(x - 3)

2x(x - 4)(x - 3)

2x(x - 4)(x + 3)

none of these

Multiple Choice

If (x + 3) divides a polynomial function evenly, then which of these is known to be a zero of the polynomial?

x = -3

x = 3

x = 0

cannot be determined

Multiple Choice

When a polynomial function f(x) is divided by
(x + 2), the remainder is 0.
What is f(-2)?

-2

cannot be determined

Multiple Choice

Factor this difference of cubes:
x³ - 343

(x + 7) (x² - 7x + 49)

(x² + 1) (x - 343)

(x - 7) (x² + 7x + 49)

(x² - 343) (x + 1)

Multiple Choice

Factor this sum of cubes:
2x³ + 128

2(x³ + 64)

(x + 4)(x² - 4x + 16)

2(x - 4)(x² + 4x + 16)

2(x + 4)(x² - 4x + 16)

Polynomial f(x) Review

Reviewing Polynomial Functions, Roots, Division, and Graphical Behavior

Show answer

Auto Play

Slide 1 / 29

SLIDE

Similar Resources on Wayground

20 questions

7.3: Exponential Growth and Decay

Presentation

•

9th - 12th Grade

19 questions

POLYNOMIAL FUNCTIONS (REVIEW)

Presentation

•

10th - 12th Grade

25 questions

Intro to probability

Presentation

•

9th - 12th Grade

22 questions

EXAMPLES Domain/Range Interval Notation

Presentation

•

9th - 12th Grade

20 questions

Polynomial factoring review

Presentation

•

10th - 12th Grade

22 questions

HL Triangle Congruence

Presentation

•

9th - 12th Grade

20 questions

Changing Percents to Decimals

Presentation

•

24 questions

Exponent Rules

Presentation

•

9th - 12th Grade

Popular Resources on Wayground

24 questions

PBIS-HGMS Day 10

Quiz

•

6th - 8th Grade

10 questions

HCS SCI 03 Summer School Review 3

Quiz

•

3rd Grade

11 questions

Home Scope

Quiz

•

7th - 8th Grade

15 questions

HCS SCI 05 Summer School Assessment 3 Review

Quiz

•

5th Grade

35 questions

Lufkin Road Middle School Student Handbook & Policies Assessment

Quiz

•

7th Grade

18 questions

Geo 11.3 Area of Circles and Sectors

Quiz

•

9th - 11th Grade

Discover more resources for Mathematics

18 questions

Geo 11.3 Area of Circles and Sectors

Quiz

•

9th - 11th Grade