Question 1

The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places.
-x3 - 8x - 3 = 0; -3 ≤ r ≤-2

Accepted Answer

Question 2

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
-$$f ( x ) = 2 x ^ { 3 } + 13 x ^ { 2 } + 10 x + 25$$

Accepted Answer

A)  $- 1 , \frac { 5 } { 2 } , 5 ; f ( x ) = ( 2 x - 5 ) ( x - 5 ) ( x + 1 )$ 
B)  $- 5 , \frac { 5 } { 2 } , 1 ; f ( x ) = ( 2 x - 5 ) ( x - 1 ) ( x + 5 )$ 
C)  $1 , \frac { 2 } { 5 } , - 5 ; f ( x ) = ( 2 x - 5 ) ( x - 1 ) ( x + 5 )$ 
D)  $- 1 , \frac { 2 } { 5 } , - 5 ; f ( x ) = ( 2 x - 5 ) ( x - 5 ) ( x + 1 )$ 
A)  $- 1 , \frac { 5 } { 2 } , 5 ; f ( x ) = ( 2 x - 5 ) ( x - 5 ) ( x + 1 )$ 
B)  $- 5 , \frac { 5 } { 2 } , 1 ; f ( x ) = ( 2 x - 5 ) ( x - 1 ) ( x + 5 )$ 
C)  $1 , \frac { 2 } { 5 } , - 5 ; f ( x ) = ( 2 x - 5 ) ( x - 1 ) ( x + 5 )$ 
D)  $- 1 , \frac { 2 } { 5 } , - 5 ; f ( x ) = ( 2 x - 5 ) ( x - 5 ) ( x + 1 )$

Question 3

List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = 2 x ^ { 5 } - 5 x ^ { 2 } + 3 x - 1$$

Accepted Answer

A)  $\pm 1 , \pm 2 , \pm \frac { 1 } { 2 }$ 
B)  $\pm 1$, $\pm 2$ 
C)  $\pm 2 , \pm \frac { 1 } { 2 }$ 
D)  $\pm 1 , \pm \frac { 1 } { 2 }$ 
A)  $\pm 1 , \pm 2 , \pm \frac { 1 } { 2 }$ 
B)  $\pm 1$, $\pm 2$ 
C)  $\pm 2 , \pm \frac { 1 } { 2 }$ 
D)  $\pm 1 , \pm \frac { 1 } { 2 }$

Question 4

Find the x- and y-intercepts of f.
-$$f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } - 1 \right)$$

Accepted Answer

A)  x-intercepts: -6, 0, 1; y-intercept: -6 
B)  x-intercepts: -1, 0, 1, 6; y-intercept: 0 
C)  x-intercepts: -6, -1, 0, 1; y-intercept: 0 
D)  x-intercepts: -6, -1, 0, 1; y-intercept: -6 
A)  x-intercepts: -6, 0, 1; y-intercept: -6 
B)  x-intercepts: -1, 0, 1, 6; y-intercept: 0 
C)  x-intercepts: -6, -1, 0, 1; y-intercept: 0 
D)  x-intercepts: -6, -1, 0, 1; y-intercept: -6

Question 5

List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 14$$

Accepted Answer

A)  $\pm 1 , \pm 7 , \pm 2 , \pm 14$ 
B)  $\pm 1 , \pm \frac { 1 } { 7 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 14 }$ 
C)  $\pm 1 , \pm 7 , \pm 2$ 
D)  $\pm 1 , \pm \frac { 1 } { 7 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 14 } , \pm 7 , \pm 2 , \pm 14$ 
A)  $\pm 1 , \pm 7 , \pm 2 , \pm 14$ 
B)  $\pm 1 , \pm \frac { 1 } { 7 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 14 }$ 
C)  $\pm 1 , \pm 7 , \pm 2$ 
D)  $\pm 1 , \pm \frac { 1 } { 7 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 14 } , \pm 7 , \pm 2 , \pm 14$

Question 6

$f ( x ) = - 2 ( x - 5 ) ^ { 5 } + 3$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 7

Solve the problem.
-The profits (in millions) for a company for 8 years was as follows: $$\begin{array} { c | c } 
\text { Year, } x & \text { Profits } \
\hline 1993,1 & 1.1 \
1994,2 & 1.7 \
1995,3 & 2.0 \
1996,4 & 1.4 \
1997,5 & 1.3 \
1998,6 & 1.5 \
1999,7 & 1.8 \
2000,8 & 2.1
\end{array}$$ Find the cubic function of best fit to the data.

Accepted Answer

The answer of Solve the problem.
-The profits (in millions) for...

Question 8

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-f(x) = -2x4 - 4x2 + 9; [-2, -1]

Accepted Answer

A)  f(-2) = 39 and f(-1) = 4; no 
B)  f(-2) = -39 and f(-1) = -3; no 
C)  f(-2) = 39 and f(-1) = -3; yes 
D)  f(-2) = -39 and f(-1) = 3; yes 
A)  f(-2) = 39 and f(-1) = 4; no 
B)  f(-2) = -39 and f(-1) = -3; no 
C)  f(-2) = 39 and f(-1) = -3; yes 
D)  f(-2) = -39 and f(-1) = 3; yes

Question 9

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$$f ( x ) = 3 - \frac { 1 } { 3 } x$$

Accepted Answer

A)  Yes; degree 1 
B)  No; x has a fractional coefficient 
C)  Yes; degree 3 
D)  Yes; degree 0 
A)  Yes; degree 1 
B)  No; x has a fractional coefficient 
C)  Yes; degree 3 
D)  Yes; degree 0

Question 10

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 11

Find the x- and y-intercepts of f.
-f(x) = (x + 6)(x - 2)(x + 2)

Accepted Answer

A)  x-intercepts: -6, -2, 2; y-intercept: -24 
B)  x-intercepts: -2, 2, 6; y-intercept: 24 
C)  x-intercepts: -2, 2, 6; y-intercept: -24 
D)  x-intercepts: -6, -2, 2; y-intercept: 24 
A)  x-intercepts: -6, -2, 2; y-intercept: -24 
B)  x-intercepts: -2, 2, 6; y-intercept: 24 
C)  x-intercepts: -2, 2, 6; y-intercept: -24 
D)  x-intercepts: -6, -2, 2; y-intercept: 24

Question 12

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
-$$f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 4 x - 12$$

Accepted Answer

A)  $- 3 ; f ( x ) = ( x + 3 ) \left( x ^ { 2 } - x - 4 \right)$ 
B)  $- 3 , - 2,2 ; f ( x ) = ( x + 3 ) ( x + 2 ) ( x - 2 )$ 
C)  $- 2 ; f ( x ) = ( x + 2 ) \left( x ^ { 2 } + x - 6 \right)$ 
D)  $- 2,2,3 ; f ( x ) = ( x + 2 ) ( x - 2 ) ( x - 3 )$ 
A)  $- 3 ; f ( x ) = ( x + 3 ) \left( x ^ { 2 } - x - 4 \right)$ 
B)  $- 3 , - 2,2 ; f ( x ) = ( x + 3 ) ( x + 2 ) ( x - 2 )$ 
C)  $- 2 ; f ( x ) = ( x + 2 ) \left( x ^ { 2 } + x - 6 \right)$ 
D)  $- 2,2,3 ; f ( x ) = ( x + 2 ) ( x - 2 ) ( x - 3 )$

Question 13

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 14

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
-$$f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 9 x - 6$$

Accepted Answer

A)  $6 ; f ( x ) = ( x - 6 ) \left( 3 x ^ { 2 } + 1 \right)$ 
B)  $3 , \frac { 2 } { 3 } , 1 ; f ( x ) = ( 3 x - 2 ) ( x - 1 ) ( x - 3 )$ 
C)  $\frac { 2 } { 3 } ; f ( x ) = ( 3 x - 2 ) \left( x ^ { 2 } + 3 \right)$ 
D)  $- 3 , - 1 , \frac { 2 } { 3 } ; f ( x ) = ( 3 x - 2 ) ( x + 1 ) ( x + 3 )$ 
A)  $6 ; f ( x ) = ( x - 6 ) \left( 3 x ^ { 2 } + 1 \right)$ 
B)  $3 , \frac { 2 } { 3 } , 1 ; f ( x ) = ( 3 x - 2 ) ( x - 1 ) ( x - 3 )$ 
C)  $\frac { 2 } { 3 } ; f ( x ) = ( 3 x - 2 ) \left( x ^ { 2 } + 3 \right)$ 
D)  $- 3 , - 1 , \frac { 2 } { 3 } ; f ( x ) = ( 3 x - 2 ) ( x + 1 ) ( x + 3 )$

Question 15

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
-$$f ( x ) = 5 x ^ { 4 } - 7 x ^ { 3 } + 22 x ^ { 2 } - 28 x + 8$$

Accepted Answer

A)  $- 4 , - 1,1 , - \frac { 2 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x + 2 ) ( x + 1 ) ( x + 4 )$ 
B)  $- 4 , - 1,1 , \frac { 2 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 2 ) ( x + 1 ) ( x + 4 )$ 
C)  $4 , \frac { 2 } { 5 } ; f ( x ) = ( x - 4 ) ( 5 x - 2 ) \left( x ^ { 2 } + 1 \right)$ 
D)  $1 , \frac { 2 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 2 ) \left( x ^ { 2 } + 4 \right)$ 
A)  $- 4 , - 1,1 , - \frac { 2 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x + 2 ) ( x + 1 ) ( x + 4 )$ 
B)  $- 4 , - 1,1 , \frac { 2 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 2 ) ( x + 1 ) ( x + 4 )$ 
C)  $4 , \frac { 2 } { 5 } ; f ( x ) = ( x - 4 ) ( 5 x - 2 ) \left( x ^ { 2 } + 1 \right)$ 
D)  $1 , \frac { 2 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 2 ) \left( x ^ { 2 } + 4 \right)$

Question 16

Find the x- and y-intercepts of f.
-$$f ( x ) = ( x + 5 ) ( x - 3 ) ( x + 3 )$$

Accepted Answer

A)  x-intercepts: -3, 3, 5; y-intercept: -45 
B)  x-intercepts: -5, -3, 3; y-intercept: -45 
C)  x-intercepts: -5, -3, 3; y-intercept: 45 
D)  x-intercepts: -3, 3, 5; y-intercept: 45 
A)  x-intercepts: -3, 3, 5; y-intercept: -45 
B)  x-intercepts: -5, -3, 3; y-intercept: -45 
C)  x-intercepts: -5, -3, 3; y-intercept: 45 
D)  x-intercepts: -3, 3, 5; y-intercept: 45

Question 17

Solve the equation in the real number system.
-$$x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17 = 0$$

Accepted Answer

A)  {-1, 4} 
B)  {-1, 1} 
C)  {-4, 4} 
D)  {-4, 1} 
A)  {-1, 4} 
B)  {-1, 1} 
C)  {-4, 4} 
D)  {-4, 1}

Question 18

f(x) = (x + 5)5

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
-$$f ( x ) = 2 x ^ { 4 } - 12 x ^ { 3 } + 19 x ^ { 2 } - 6 x + 9$$

Accepted Answer

A)  $- 3,3 ; f ( x ) = ( x - 3 ) ( x + 3 ) \left( 2 x ^ { 2 } + 1 \right)$ 
B)  no real roots; $f ( x ) = \left( x ^ { 2 } + 9 \right) \left( 2 x ^ { 2 } + 1 \right)$ 
C)  3 , multiplicity $2 ; f ( x ) = ( x - 3 ) ^ { 2 } \left( 2 x ^ { 2 } + 1 \right)$ 
D)  $- 3$, multiplicity $2 ; f ( x ) = ( x + 3 ) ^ { 2 } \left( 2 x ^ { 2 } + 1 \right)$ 
A)  $- 3,3 ; f ( x ) = ( x - 3 ) ( x + 3 ) \left( 2 x ^ { 2 } + 1 \right)$ 
B)  no real roots; $f ( x ) = \left( x ^ { 2 } + 9 \right) \left( 2 x ^ { 2 } + 1 \right)$ 
C)  3 , multiplicity $2 ; f ( x ) = ( x - 3 ) ^ { 2 } \left( 2 x ^ { 2 } + 1 \right)$ 
D)  $- 3$, multiplicity $2 ; f ( x ) = ( x + 3 ) ^ { 2 } \left( 2 x ^ { 2 } + 1 \right)$

Question 20

List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = 6 x ^ { 4 } + 4 x ^ { 3 } - 2 x ^ { 2 } + 2$$

Accepted Answer

A)  $\pm \frac { 1 } { 2 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
B)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2$ 
C)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2 , \pm 3$ 
D)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2$ 
A)  $\pm \frac { 1 } { 2 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
B)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2$ 
C)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2 , \pm 3$ 
D)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2$

The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. -x³ - 8x - 3 = 0; -3 ≤ r ≤-2

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 2 x ^ { 3 } + 13 x ^ { 2 } + 10 x + 25$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = 2 x ^ { 5 } - 5 x ^ { 2 } + 3 x - 1$

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } - 1 \right)$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 14$

$f ( x ) = - 2 ( x - 5 ) ^ { 5 } + 3$ $f ( x ) = - 2 ( x - 5 ) ^ { 5 } + 3$

Solve the problem. -The profits (in millions) for a company for 8 years was as follows: Year, x Profits 1993,1 1.1 1994,2 1.7 1995,3 2.0 1996,4 1.4 1997,5 1.3 1998,6 1.5 1999,7 1.8 2000,8 2.1 Find the cubic function of best fit to the data.

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. -f(x) = -2x⁴ - 4x² + 9; [-2, -1]

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 3 - \frac { 1 } { 3 } x$

Find the x- and y-intercepts of f. -f(x) = (x + 6)(x - 2)(x + 2)

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 4 x - 12$

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 9 x - 6$

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 5 x ^ { 4 } - 7 x ^ { 3 } + 22 x ^ { 2 } - 28 x + 8$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 5 ) ( x - 3 ) ( x + 3 )$

Solve the equation in the real number system. - $x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17 = 0$

f(x) = (x + 5)⁵

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 2 x ^ { 4 } - 12 x ^ { 3 } + 19 x ^ { 2 } - 6 x + 9$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = 6 x ^ { 4 } + 4 x ^ { 3 } - 2 x ^ { 2 } + 2$

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Exam 3: Polynomial and Rational Functions

The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. -x3 - 8x - 3 = 0; -3 ≤ r ≤-2

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - f(x)=2x3+13x2+10x+25f ( x ) = 2 x ^ { 3 } + 13 x ^ { 2 } + 10 x + 25f(x)=2x3+13x2+10x+25

List the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=2x5−5x2+3x−1f ( x ) = 2 x ^ { 5 } - 5 x ^ { 2 } + 3 x - 1f(x)=2x5−5x2+3x−1

Find the x- and y-intercepts of f. - f(x)=−x2(x+6)(x2−1)f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } - 1 \right)f(x)=−x2(x+6)(x2−1)

List the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=x5−4x2+3x+14f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 14f(x)=x5−4x2+3x+14

f(x)=−2(x−5)5+3f ( x ) = - 2 ( x - 5 ) ^ { 5 } + 3f(x)=−2(x−5)5+3

Solve the problem. -The profits (in millions) for a company for 8 years was as follows: Year, x Profits 1993,1 1.1 1994,2 1.7 1995,3 2.0 1996,4 1.4 1997,5 1.3 1998,6 1.5 1999,7 1.8 2000,8 2.1 Find the cubic function of best fit to the data.

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. -f(x) = -2x4 - 4x2 + 9; [-2, -1]

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - f(x)=3−13xf ( x ) = 3 - \frac { 1 } { 3 } xf(x)=3−31​x

Find the x- and y-intercepts of f. -f(x) = (x + 6)(x - 2)(x + 2)

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - f(x)=x3+3x2−4x−12f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 4 x - 12f(x)=x3+3x2−4x−12

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - f(x)=3x3−2x2+9x−6f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 9 x - 6f(x)=3x3−2x2+9x−6

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - f(x)=5x4−7x3+22x2−28x+8f ( x ) = 5 x ^ { 4 } - 7 x ^ { 3 } + 22 x ^ { 2 } - 28 x + 8f(x)=5x4−7x3+22x2−28x+8

Find the x- and y-intercepts of f. - f(x)=(x+5)(x−3)(x+3)f ( x ) = ( x + 5 ) ( x - 3 ) ( x + 3 )f(x)=(x+5)(x−3)(x+3)

Solve the equation in the real number system. - x4−8x3+16x2+8x−17=0x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17 = 0x4−8x3+16x2+8x−17=0

f(x) = (x + 5)5

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - f(x)=2x4−12x3+19x2−6x+9f ( x ) = 2 x ^ { 4 } - 12 x ^ { 3 } + 19 x ^ { 2 } - 6 x + 9f(x)=2x4−12x3+19x2−6x+9

List the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=6x4+4x3−2x2+2f ( x ) = 6 x ^ { 4 } + 4 x ^ { 3 } - 2 x ^ { 2 } + 2f(x)=6x4+4x3−2x2+2

Functions and Their Graphs

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The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. -x³ - 8x - 3 = 0; -3 ≤ r ≤-2

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 2 x ^ { 3 } + 13 x ^ { 2 } + 10 x + 25$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = 2 x ^ { 5 } - 5 x ^ { 2 } + 3 x - 1$

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } - 1 \right)$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 14$

$f ( x ) = - 2 ( x - 5 ) ^ { 5 } + 3$ $f ( x ) = - 2 ( x - 5 ) ^ { 5 } + 3$

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. -f(x) = -2x⁴ - 4x² + 9; [-2, -1]

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 3 - \frac { 1 } { 3 } x$

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 4 x - 12$

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + 9 x - 6$

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 5 x ^ { 4 } - 7 x ^ { 3 } + 22 x ^ { 2 } - 28 x + 8$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 5 ) ( x - 3 ) ( x + 3 )$

Solve the equation in the real number system. - $x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17 = 0$

f(x) = (x + 5)⁵

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 2 x ^ { 4 } - 12 x ^ { 3 } + 19 x ^ { 2 } - 6 x + 9$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = 6 x ^ { 4 } + 4 x ^ { 3 } - 2 x ^ { 2 } + 2$