MAC1140 Exam 2

What is the domain of the real-valued function f(x)= -13 6sqrt(-3x+17)-1

(-infinity, 17/3]

What is the result when dividing 2x^5-13x^4+11x^3+8x^2+5x-12 by 2x-3?

x^4-5x^3-2x^2+x+4

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

(-inf, inf)

what is the domain of the real-valued function f(x)=2sqrt(-x+1)+7

(-infinity, 1]

Which of the following is the graph of f(x) = (-x+2)^3-1

negative graph zero at 0,1

Consider the polynomial p(x) =-2x^9+4x^8+3x^4-2x^3-x^2. 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

Which of the following is an inverse of the function f(x) = x^3+3x^2+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)=3sqrt(y-1)

Which of the following is an inverse of the function f(x)=x^2+4x+18, with the largest valid domain of f(x) that is inverted.

f(x) is inverted on the domain x gr/= and the inverse function is f^-1(y)= sqrt(y-14)-2

Simplify the numeric radical sqrt(2695)

7sqrt(55)

Simplify the numeric radical sqrt(486)

9sqrt(6)

Within which of the following segments is the function increasing and concave down?

Between b and c

What values of x satisfy the equation: sqrt(10x-15)= sqrt(8x-16) + 1

x=4

Which of the following is equivalent to the expression sqrt(125x^3y^6) - sqrt(5x)

(5|xy^3|-1)sqrt(5x)

Fully factor the following polynomial: x^2-22x+121

(x-11)^2

What is the fully factored form for the polynomial f(x)=x^4-256

(x-4)(x+4)(x^2+16)

What is the remainder when -4x^4+x^3+11x^2-3x-1 is divided by -x-3?

-244

What is the remainder when x^4-x^3-19x^2+47x-25 is divided by x^2+2x-15

-2x+5

Consider the polynomial p(x)= 4x^3+16x^2-25x-100. What is the sum of the zeros of p(x)?

-4

Fully factor the following polynomial: -4x^2-12x+16

-4(x+4)(x-1)

Consider the polynomial p(x)=45x^3+69x^2-24x-48. What are the real valued zeroes of p(x)

-4/5, -1, 4/5

Consider the polynomial p(x)=45x^3+69x^2-24x-48. What are the zeros of 3p(x+1)?

-7/3, -2,-1/5

Consider the function p(x) =-3x^12-4x^19+3x^9+2x. Which of the following below values are a possible number of absolute extrema for this function?

0

Consider the function 5x^13-10x^8+7x^15+x^19 Which of the below values are a possible number of relative extrema for this function?

0, 12,18

Consider the polynomial p(x)= 14x^3+7x^2+9x+323 Which of the following can not be a root of the polynomial?

17x-7

Consider the polynomial p(x)= -13x^12-4x^19+3x^9+2x How many zeros does this polynomial have including complex valued zeros and counting multiplicity?

19

Fully factor the polynomial: 25x^4-50x^2+25

25(x-1)^2(x+1)^2

Which of the following is the fully simplified form of 3sqrt(120x^4(x+2)^5)

2x(x+2)3sqrt(15x(x+2)^2)

Full factor the polynomial 6x^5-8x^4-54x^3+72x^2

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

Consider the polynomial p(x)= 45x^3+69x^2-24x-48. How many roots does this polynomial have counting multiplicity?

3

Fully factor the following polynomial: 9x^6-64

3sqrt(3x-2)(3s

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

Simplify the numberic radical 5sqrt(3125)

5

Which of the following is equivalent to sqrt(375x^6(x+2)^3)

5x^3(x+2)sqrt(15(x+2))

Fully factor the following polynomial: 9x^3-72

9(x-2)(x^2+2x+4)

Which of the following is the best definition for monomial?

A term of the form ax^n for some constant a and some non-negative integar n

Which of the following is the best definition for binomial?

An expression that is the sum or difference of two monomials.

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

An irreducible polynomial that is a factor of the given polynomial.

Which of the following is the best definition for Polynomial?

Any function or expression that is entirely composed of terms of the form ax^n.

Which of the following equations are polynomials? I: f(x)= x^2+1 II: g(x)=13x^3+7 III: h(x)=7 IV: k(x)=x^3+3x^1/3+1

I,II and III only

Which of the following is the best definition for leading term(of a polynomial)?

The term with the highest power and its coefficient

simplify the expression 4sqrt(x^4-16)

This is already simplified as can be

Simplify the expression sqrt(x^4-81)

This is already simplified as it can be

Simplify the expression 3sqrt(x^6-27)

This is already simplified.

Consider the polynomial p(x)=x^4-4x^3-47x^2+210x. Which of the following are true? I: p(x) is degree 4 II: p(x) has 4 real zeroes III: The sum of the zeroes of p(x) is 4 IV: The product of the zeroes of p(x) is o

all of these are correct

if 0< a<1 is there an integer n such that n(sqrta) gr/= 1

no

Which value(s) of x satisfy the equation sqrtx - sqrt(x+4)=2

no real solutions

Before simplifying the radical sqrt(3x^3-25x^2+24x+28), one should convert it to which of the following?

sqrt((3x+2)(x-2)(x-7)

Factor the radicand of the following radical: sqrt( 2x^2+15x+28)

sqrt(2x+7)(x+4)

If a<b must it be true that 3sqrt(a) < 3sqrt(b)

true

What values of x satisfy the equation: sqrt(9x-9/4)= sqrt(5x-25/4) + 2

x=5/2