PRACTICE EXAM 2 ANSWERS OP

Which of the following is the best definition for Binomial?

An expression that is the sum or difference of two monomials. From "bi" meaning "two".

Before simplifying the radical √3x³ -25x² + 24x + 28

√(3x + 2) (x - 2) (x - 7)

Before simplifying the radical √3x³ -25x² +24x + 28, one should convert it to which of the following?

√(3x+2) (x-2) (x-7)

Fully factor the following polynomial: 9𝑥³ − 72

9 (x - 2) (x² + 2x + 4)

What is the domain of the real-valued (ie no non-real numbers allowed) function f(x) = 2 √-x + 1 + 7 ?

(-∞, 1]

What is the domain of the radical function 𝑓(𝑥) = ³√-x-1

(-∞, ∞)

Which of the following is equivalent to the expression √125x³y⁶ - √5x ?

(5 | 𝑥𝑦 | - 1) √5x (FIGURE OUT HOW TO GET ANSWER FOR THIS)

Fully factor the following polynomial: 10𝑥² −8𝑥 −18

(5x-9)(2x+2)

Consider the polynomial 𝑝(𝑥) = 14𝑥³ + 7𝑥² +9𝑥 + 323. According to the rational root test, which of the following is NOT a possible zero of p(x)?

(CLICK USE THE RATIONAL ROOTS TEST TO FIND ALL POSSIBLE ROOTS) X= 7/19

What is the fully factored form (with real coefficients) for the polynomial 𝑓(𝑥) = 𝑥⁴ − 256

(𝑥 − 4) (𝑥 + 4) (𝑥² + 16)

What is the primary difference between even and odd roots? Select all of the below that are true.

- Odd roots are inverses to potentially one to one functions which means it can have a domain of all real numbers and doesn't need absolute values. -Even roots must use restricted domains to get a partial inverse of an even power which leads to a host of nuance issues like absolute values and domain problems.

What is the remainder when −4𝑥⁴ +𝑥³ +11𝑥² −3𝑥−1 is divided by −𝑥−3?

-244

What is the remainder when 𝑥⁴ −𝑥³ − 19𝑥² + 47𝑥 − 25 is divided by 𝑥² + 2𝑥 − 15

-2x + 5

Consider the polynomial 𝑝(𝑥)=4𝑥3+16𝑥2−25𝑥−100. What is the sum of the zeros of p(x)?

-4

Consider the polynomial p(𝑥 )= 4𝑥³ +16𝑥² − 25𝑥 − 100. What is the sum of the zeros of 𝑝(𝑥)?

-4

Consider the polynomial 𝑝(𝑥)=45𝑥³ +69𝑥² −24𝑥 −48 What are the zeros of 3𝑝(𝑥 + 1)?

-7/3 , -2, -7/3

Consider the function 𝑝(𝑥)= −3𝑥¹² −4𝑥¹⁹ + 3𝑥⁹ +2𝑥. Which of the below values are a possible number of absolute extrema for this function? (Select all that apply!)

0

Consider the polynomial 𝑝(𝑥) = −9𝑥⁸ −5𝑥⁸ −4𝑥¹³ −3𝑥. How many zeros does this polynomial have including complex valued zeros and counting multiplicity?

13

Consider the polynomial, 𝑝(𝑥) = −13𝑥¹² − 4𝑥¹⁹ + 3𝑥⁹ +2𝑥 How many zeros does this polynomial have including complex valued zeros and counting multiplicity?

19

Fully factor the following polynomial: 25𝑥⁴ − 50𝑥² +25

25(x - 1)² (x + 1)²

Which of the following is the fully simplified form of ³√120x⁴ (x + 2)⁵?

2x (x + 2) ³√15x (x + 2)²

Full factor the polynomial 6𝑥⁵ −8𝑥⁴ −54𝑥³ + 72𝑥²

2x² (3x-4) (x-3) (x+3)

Consider the polynomial 𝑝(𝑥) = 45𝑥³ + 69𝑥² −24𝑥 − 48. How many roots does this polynomial have counting multiplicity?

3

Consider the following graph of 𝑓(𝑥): Based on the number of extrema, what is the smallest degree possible for the leading term of 𝑓?

4 (two arrows going up letters a-e)

Simplify the numeric radical ³√2160

6³√10

Simplify the numeric radical √2695

7 √55

Fully factor the polynomial: 24𝑥³ −8𝑥² −96𝑥 + 32

8 (x-2)(x+2)(3x-1)

Simplify the numeric radical √486

9√6

Which of the following is the best definition for Monomial?

A term of the form axⁿ for some constant "a" and some non-negative integer "n."

Consider the polynomial 𝑝(𝑥)= 𝑥⁴ − 4𝑥³ − 47𝑥² +210𝑥 Which of the following are true? I: 𝑝(𝑥) is degree 4. II: 𝑝(𝑥) has 4 real zeros. III: The sum of the zeros of 𝑝(𝑥) is 4. IV: The product of the zeros of 𝑝(𝑥) is 0.

All of these are correct. something similar? use find the roots, count how many you. see and pick every answer with that number

Which of the following equations are polynomials? I: 𝑓(𝑥)= 𝑥²+1 II: 𝑔(𝑥)= 13𝑥³ + 7 III: ℎ(𝑥) = 7 IV: 𝑘(𝑥) = 𝑥³+3𝑥¹3+1

I, II, and III Only.

Consider the polynomial p(x) = 4𝑥⁶ − 6𝑥⁵ + 2𝑥⁴− 3𝑥³ − 12𝑥² +18𝑥 and the following techniques from class; I: Rational Root Theorem II: Completing the Square III: Synthetic Division IV: Factor by Grouping V: AC-Method Which of the previous techniques are possible techniques one could use as the first factoring technique on 𝑝(𝑥) (In other words, which of the above can you apply directly to p(x) without any additional techniques, to factor p(x) into the product oftwo or more polynomials.)

IV. Factor by grouping.

Consider the polynomial 𝑓(𝑥)=𝑥² +3𝑥 +2. Which of the following statements are true? I: 𝑓(𝑥) has 2 roots but no real zeros. II: 𝑓(𝑥) has 2 roots and 2 real zeros. III: 𝑓(𝑥) is degree 2 which is why it must have 2 real zeros. IV: 𝑓(𝑥) is degree 2 but has no real zeros.

Only II is correct.

Which of the following is the best definition for Leading Term (of a polynomial)?

The term with the highest power and it's coefficient

Simplify the expression: √x⁴ - 81

This is already as simplified as it can be

Simplify the expression ³√x⁶ - 27

This is already as simplified as it can be.

Consider the following graph of f(x): Within which of the following segments is the function increasing and concave down?

between b and c

Which of the following is an inverse of the function f (x) = x² + 4x + 18 with the largest valid domain of 𝑓(𝑥) that is inverted.

f(x) is inverted on the domain x ≥ -2, and the inverse function is f⁻¹ (y) = y - 14 - 2. FIGURE*

Which value(s) of x Satisfy the equation. √x - √x + 4 = 2

no real solutions

If 𝑎 < 𝑏 must it be true that ³√𝑎 < ³√𝑏

true

Which real value(s) of 𝑥 satisfy the equation √4x + 3 = 2 √x - 1 + 1

x = 13/4

What value(s) of 𝑥 satisfy the equation: √9x - 9/4 = √5x - 25/4 + 2

x= 5/2

What is the result when dividing 2𝑥⁵ − 13𝑥⁴ +11𝑥³ + 8𝑥² + 5𝑥 −12 BY 2x-3

x⁴ - 5x³- 2x² + x + 4

Factor the radicand of the following radical: √2x² +15x +28

√(2x+7) (x+4)

Which of the following is equivalent to the expression: √-18x³ +3x² +54x +24

√-3 (3x +4)(2x+1)(x-2)

Which of the following is an inverse of the function 𝑓(𝑥) = 𝑥³ +3 𝑥² + 3𝑥 + 1 with the largest valid domain of 𝑓(𝑥) that is inverted.

𝑓(𝑥) is inverted on the domain all real numbers, and the inverse function is f⁻¹ (y) = ³√y - 1

Consider the polynomial 𝑝(𝑥)= −2𝑥⁹ + 4𝑥⁸ + 3𝑥⁴ −2𝑥³ −𝑥²

𝑝(𝑥) does not have an absolute extrema and it has at most 8 local extrema.

Consider the polynomial 𝑝(𝑥)= −2𝑥⁹ +4𝑥⁸ +3𝑥⁴ −2𝑥³ −𝑥² . What can be said about the extrema of 𝑝(𝑥)?

𝑝(𝑥) does not have an absolute extrema and it has at most 8 local extrema.