EOC Review #2

EOC Review #1

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Multiple Choice

Find all the real zeros

f(x) = 2x³ + 5x² − 6x − 9.

Hint: real zeros are x intercepts,

try graphing in Desmos.

• −1, -3, -3

• −1, -3, 3/2

• 3, 3, 3,

• −3, 2/3, 1

Multiple Choice

Which could be this graph?

Hint: look at your roots, multiplicity, and end behavior!!

• y = ^_(x + 4)(x - 2)²

• y = -(x - 4)(x + 2)²

• y = (x - 4)(x + 2)²

• y = -x³

Multiple Select

What is a local or relative maximum(s)?

• (−3,2)

• (2, 1)

• (−1,−3)

• (4, −1)

• there is no local maximum

​The leading coefficient tells you what happens as the x's get bigger.

​

​The degree being even or odd tells you whether the other is the same or different

Multiple Choice

Which best describes the graph?

Hint: What happens to the y's as the x's get bigger?Are the end behaviors the same or different

• Leading Coefficient Positive

  Degree - Even

• Leading Coefficient Positive

  Degree - Odd

• Leading Coefficient Negative

  Degree - Even

• Leading Coefficient Negative

  Degree - Odd

Multiple Choice

The function shown has:

Hint: Are the end behaviors the same or not? What is happening to the y's as the x's get bigger?

• Degree two with negative leading coefficient.

• Degree three with negative leading coefficient.

• Degree four with negative leading coefficient.

• Degree four with positive leading coefficient.

Multiple Choice

Which is equilvalent?

x³ + 1

hint: graph the first one in Desmos,

Then find the answer choice the makes the same graph

• (x + 1)³

• (x+1)(x² - x + 1)

• (x - 1) (x² + x - 1)

• (x + 1)(x² - 2x + 1)

Multiple Choice

Which is equivalent

8x³ - 1

hint: graph the first one in Desmos,

Then find the answer choice the makes the same graph

• (2x -1)(4x² +2x +1)

• (2x +1)(4x² - 2x+ 1)

• (2x -1)(4x² -2x - 1)

• (2x +1)(4x² +2x +1)

synthetic division

• only used when dividing by x plus or minus a number

• put the opposite of the number on the shelf

• write the coefficients, use 0 for missing terms

• bring down the first one

• Multiply , Bring over and then add

• put the variables back, remainder over divisor

Polynomial Long division

For the EOC

-type the question on one line

-type the answer choices on separate lines.

-the question and the correct answer are equivalent and will make identical graphs

5x²+3x-2÷(x+1)

Multiple Choice

find the equivalent expression.

Hint: enter the problem on one line in Desmos

and find the answer choice that makes the same graph.

• 2x - 4

• 2x + 4

• 2x - 1 + -16/4x-5

• 2x - 4 + -40/4x-5

Multiple Choice

find the equivalent expression.

Hint: enter the problem on one line in Desmos

and find the answer choice that makes the same graph.

(3x³ + 5x - 1) ÷ (x + 1)

• 3x³ - 3x² + 8x - 9

• $$3x^2-3x+8-\frac{9}{x+1}$$

• $$3x^2+3x+8+\frac{7}{x+1}$$

• 3x³ + 3x² + 8x + 7

​Use this when you just need to know the remainder,

or

​whether a binomial is a factor

​because if the remainder is zero when you divide two polynomials, they must be factors.

​

Multiple Choice

What is the remainder when a³ − 4 is divided by a +2?

• −2

• −6

• −12

• 0

Multiple Choice

What is the remainder of  (3x³ -5x² -4x +1) ÷ (x + 3)?

• -25

• 25

• 113

• -113

Multiple Choice

Is (x-3) a factor of
(x³ - 3x² + 2x + 2)?

• Yes

• No

If (x -2) is a factor of f(x)=x³+4x²−5x−k

Find k

• 0 = (2)³+4(2)²−5(2)−k

• 0 = 14 − k

• k = 14

Multiple Choice

For the following polynomial, k is an integer.

y = x³ + 4x² - 11x + k

If (x + 5) is a factor, find k

• k = −10

• k = −20

• k = −30

• k = −40

​When adding polynomials:

​-combine like terms

​

​When subtracting polynomials:

​-distribute the negative 1 and then combine like terms

​

​When multiplying monomials:

​-multiply the coefficients and add the exponents.

Multiple Choice

f(x) = 3x² + 7x and g(x) = 2x² - x - 1,

find (f + g)(x).

hint: enter in Desmos y = (3x² + 7x) + (2x² - x - 1)

Find the expression that makes the same graph

• 11x² - 1

• 5x⁴ + 6x² - 1

• 5x² + 6x - 1

• 5x² + 8x - 1

Multiple Choice

Given  $$f\left(x\right)=3x^2-2x+1$$  and  $$g\left(x\right)=2x$$  ,

find  $$\left(f\times g\right)\left(x\right)$$  

hint: enter in Desmos y = (3x² - 2x + 1) (2x)

Find the expression that makes the same graph

• $$6x^2-4x-2$$  

• $$6x^3-4x^2-2x$$  

• $$6x^3+4x^2+2x$$  

• $$5x^3+4x^2-9x-4$$  

Multiple Choice

f(x) = 3x² + 7x and g(x) = 2x² - x - 1,

find (f - g)(x).

hint: enter in Desmos y = (3x² + 7x) - (2x² - x - 1)

Find the expression that makes the same graph

• x² + 8x + 1

• x² + 6x - 1

• 5x² + 8x - 1

• x² + 8x -1

Remember to always use the x part of the coordinates to describe when the interval begins and ends for increasing , decreasing or constant

Multiple Choice

This graph is decreasing on the intervals...

• ( -∞, -2 ) U ( 2, ∞ )

• ( -∞, 0 ) U ( 4, ∞ )

• ( -2, 2 )

• ( 0, 4 )

Multiple Choice

This graph increases from...

• ( -1, 1 )

• ( 0, 4 )

• (-1, 4 )

• [ 0, 4 ]

Zeros or Roots

• The degree of a polynomial gives you the total number of zeros, real or complex, it has.

• real zeros are x intercepts

• complex zeros always come in pairs, always an even number

Zeros or Roots

• each real zero, x intercept, may have different multiplicities

Multiplicity- number of times a factor results in a zero

Multiplicity of 1

graphs goes straight through the x axis

Multiplicity of 2

graphs bounces off the x axis

Multiplicity of 3

graphs flattens out and then goes through the x axis

Zeros and Multiplicity

Make sure you count correctly when the multiplicity is not 1

Multiple Choice

How many rzeros does this polynomial have?

• 0

• 2

• 3

• 5

Multiple Choice

Graph and find all the rational zeros

f(x) = 2x³ + 5x² − 6x − 9

• −1, −3, -3

• −1, -3, 1.5

• 0, 3, 3

• −3, 2.5, 4

Multiple Choice

What are the

zeros of the polynomial

y = (x + 4)(x + 1)(3x − 6)?

• −4, −1, 2

• 3, −3, 4, 1

• 4, 1, −6

• 3, −4, −1, 6

Multiple Choice

Find all the real zeros of the function

f(x) = 2x³ − 19x² + 38x + 24

• x = 1/2, −6

• x = −1/2, 6

• x = 4, −1/2, 6

• x = −4, 1/2, −6

Multiple Choice

Match the equation to the graph.

• $$y=\left(x+4\right)\left(x-1\right)\left(x-2\right)$$

• $$y=\left(x-4\right)\left(x-1\right)\left(x+2\right)$$

• $$y=\left(x+4\right)\left(x+1\right)\left(x-2\right)$$

Multiple Choice

Which equation best fits the graph?

• y = x(x − 3)(x − 2)

• y = x(x − 3)² (x + 2)

• y = x(x + 3)² (x − 2)

Multiple Choice

This is an example of "which is equivalent"

Type the original in Desmos the way it is or make it multiplication and flip what we are dividing by.

Find the expression that matches

• a

• b

• c

• d

Multiple Choice

This is an example of "which is equivalent"

Type the original in Desmos changing the a's to x's

Find the expression that matches the graph

Multiple Choice

This is an example of "which is equivalent"

Type the original in Desmos changing the a's to x's

Find the expression that matches the graph

Multiple Choice

solve

Hint: you cn solve any equation in Desmos,

Enter each side of the equal sign with y = on a line in Desmos, changing the letter to x.

The x of the intersection point is the solution

• -3

• 3

• 4

• -4

Multiple Choice

Solve

Hint: you cn solve any equation in Desmos,

Enter each side of the equal sign with y = on a line in Desmos, changing the letter to x.

The x of the intersection point is the solution

• 11

• 5

• 8

• 7

Together or alone work problems

After writing the equation, solve using Desmos.

Multiple Choice

After a heavy snowfall, Brian can shovel all of the driveway in 30 minutes. If his younger brother Allen helps, the job takes only 20 minutes. How long would it take Allen to do the job by himself?

• 60 minutes

• 45 minutes

• 50 minutes

• 555 minutes

Multiple Choice

Tim can paint the football field in 8 hours. JaQuii can paint the football field in 6 hours. Damien can paint the field in 4 hours. How long does it take them to paint the field together? 

• It will take them 24 hours. 

• It will take them 1.8 hours. 

• It will take them 11 hours. 

• It will take them 2.4 hours.