Question 1

Use the graph of the polynomial function f(x) to solve f( $$f ( x ) \text { to solve } f ( x ) = 0$$
-
A) 0,2
B) $- 2$
C) $- 2,0$
D) 0

Accepted Answer

The answer of Use the graph of the polynomial function...

Question 2

Use factoring and the root method to solve the polynomial equation.
-$0.1 \mathrm { x } ^ { 3 } - 9 \mathrm { x } = 0$
A) $- 3 \sqrt { 10 } , 0,3 \sqrt { 10 }$
B) $- 9 \sqrt { 10 } , 0,9 \sqrt { 10 }$
C) $0,3 \sqrt { 10 }$
D) $- 9 \sqrt { 10 } , 9 \sqrt { 10 }$

Accepted Answer

First, factor out an $x$, getting $x(0.1x^2 - 9) = 0$. This gives us one root, $x = 0$. For the quadratic, set $0.1x^2 - 9 = 0$, solve for $x^2$, getting $x^2 = 90$, and thus $x = \pm \sqrt{90} = \pm 3\sqrt{10}$.

Question 3

Solve the polynomial equation by using the root method.
-$$4 x ^ { 3 } - 108 = 0$$
A) $3 , - 3$
B) 3,0
C) $- 3$
D) 3

Accepted Answer

To solve the polynomial equation $4x^3 - 108 = 0$, we first add 108 to both sides to get $4x^3 = 108$. Then, we divide both sides by 4 to get $x^3 = 27$. Taking the cube root of both sides gives $x = 3$, which is the only solution.

Question 4

Use factoring by grouping to solve the equation.
-$$2 x ^ { 3 } + 8 x ^ { 2 } - 8 x - 32 = 0$$
A) $- 4 , - 2,1$
B) $- 4 , - 2,2$
C) $- 8 , - 4,4$
D) $- 2,2,4$

Accepted Answer

Factoring by grouping: $2x^2(x + 4) - 8(x + 4) = 0$ gives $(2x^2 - 8)(x + 4) = 0$. Solving gives roots $x = -4, -2, 2$.

Question 5

Use factoring and the root method to solve the polynomial equation.
-$$x ^ { 4 } - 6 x ^ { 2 } + 9 = 0$$
A) 3
B) $- 3,3$
C) $\sqrt { 3 }$
D) $- \sqrt { 3 } , \sqrt { 3 }$

Accepted Answer

This polynomial equation can be factored as a perfect square trinomial: $(x^2 - 3)^2 = 0$. Setting each factor equal to zero gives $x^2 - 3 = 0$, which solves to $x^2 = 3$. Taking the square root of both sides gives $x = \pm \sqrt{3}$, which corresponds to choice D.

Question 6

Solve the polynomial equation by using the root method.
-$$\frac { 1 } { 2 } x ^ { 3 } + 4 = 0$$
A) $2 , - 2$
B) $- 2$
C) 2,0
D) 2

Accepted Answer

The answer of Solve the polynomial equation by using the...

Question 7

Use the graph of the polynomial function f(x) to solve f( $$f ( x ) \text { to solve } f ( x ) = 0$$
-
A) $- 2 , \frac { 1 } { 2 } , 3$
B) $- 2,3$
C) $- 3,2$
D) $- 3 , - \frac { 1 } { 2 } , 2$

Accepted Answer

The answer of Use the graph of the polynomial function...

Question 8

Use factoring by grouping to solve the equation.
-$$x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32 = 0$$
A) $- 4 , - 2,2$
B) $2 , - 4,4$
C) $- 2,2,4$
D) $- 2 , - 4,4$

Accepted Answer

The equation can be factored by grouping: $(x^3 + 2x^2) + (-16x - 32) = x^2(x + 2) - 16(x + 2) = (x^2 - 16)(x + 2)$. Further factoring gives $(x - 4)(x + 4)(x + 2) = 0$, leading to roots $x = 4, x = -4, x = -2$.

Question 9

Use the graph of the polynomial function f(x) to solve f( $$f ( x ) \text { to solve } f ( x ) = 0$$
-
A) $- 6 , - 2,4$
B) 2,4
C) $- 6 , - 2$
D) $- 4,2,6$

Accepted Answer

The answer of Use the graph of the polynomial function...

Question 10

Use the graph of the polynomial function f(x) to solve f( $$f ( x ) \text { to solve } f ( x ) = 0$$
-
A) $- 3,2,4$
B) $- 3 , - 1,2,4$
C) $- 4 , - 2,3$
D) $- 4 , - 2,1,3$

Accepted Answer

The answer of Use the graph of the polynomial function...

Question 11

Use factoring and the root method to solve the polynomial equation.
-$11 x ^ { 4 } - 33 x ^ { 2 } = 0$
A) $- \sqrt { 3 } , \sqrt { 3 }$
B) $0 , - 3,3$
C) $0 , - \sqrt { 3 } , \sqrt { 3 }$
D) $0 , \sqrt { 3 }$

Accepted Answer

First, factor out the common term, which is $11x^2$, to get $11x^2(x^2 - 3) = 0$. Setting each factor equal to zero gives $x^2 = 0$ and $x^2 - 3 = 0$. Solving these equations gives $x = 0$, $x = \sqrt{3}$, and $x = -\sqrt{3}$.

Question 12

$6 x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } = 0$
A) -1,-1,0 
B)  1,-1,0 
C)  1,1,0 
D)  -1,1

Accepted Answer

The equation can be factored as $6x^2(x^2 + 2x + 1) = 0$, simplifying to $6x^2(x + 1)^2 = 0$. The roots are $x = 0$ and $x = -1$ (with a multiplicity of 2 for -1), matching choice A.

Question 13

Solve the polynomial equation by using the root method.
-$$3 x ^ { 4 } - 768 = 0$$
A) $- 4$
B) 4,0
C) $4 , - 4$
D) 4

Accepted Answer

The equation can be rewritten as $3x^4 = 768$. Dividing both sides by 3 gives $x^4 = 256$. Taking the fourth root of both sides gives $x = \pm 4$, since both 4 and -4 raised to the fourth power equal 256.

Question 14

Use the graph of the polynomial function f(x) to solve f( $$f ( x ) \text { to solve } f ( x ) = 0$$
-
A) $- 4 , - 1,1,4$
B) $- 3 , - 1$
C) $- 3 , - 1,1,3$
D) 1,3

Accepted Answer

The answer of Use the graph of the polynomial function...

Question 15

Solve the polynomial equation by using the root method.
-$$\frac { 1 } { 5 } x ^ { 4 } - 125 = 0$$
A) $5 , - 5$
B) $- 5$
C) 5
D) 5,0

Accepted Answer

The equation can be rewritten as $x^4 = 625$. Taking the fourth root of both sides gives $x = \pm 5$, hence both 5 and -5 are solutions.

Question 16

A)  -2,3 
B)  -2,0,3 
C)  -3,2 
D)  -3,0,2

Accepted Answer

The answer of 
A)  -2,3 
B)  -2,0,3 
C)...

Question 17

$x ^ { 4 } - 18 x ^ { 2 } + 32 = 0$
A) 16,2
B) 16, $\pm \sqrt { 2 }$
C) 4, $\sqrt { 2 }$
D) $\pm 4 , \pm \sqrt { 2 }$

Accepted Answer

This equation can be solved by substituting $y = x^2$, turning it into a quadratic equation $y^2 - 18y + 32 = 0$. Solving this quadratic equation yields $y = 16$ and $y = 2$. Substituting back $x^2 = y$, we get $x^2 = 16$ which gives $x = \pm 4$, and $x^2 = 2$ which gives $x = \pm \sqrt{2}$.

Question 18

Use factoring by grouping to solve the equation.
-$$5 x ^ { 3 } + 3 x ^ { 2 } - 125 x - 75 = 0$$
A) $- 5,5 , \frac { 3 } { 5 }$
B) $- \frac { 5 } { 3 } , - 5,1$
C) $- \frac { 3 } { 5 } , - 5,5$
D) $- \frac { 5 } { 3 } , - 5,5$

Accepted Answer

First, factor by grouping: $5x^3 + 3x^2 - 125x - 75 = x^2(5x + 3) - 25(5x + 3) = (x^2 - 25)(5x + 3)$. Then, factor further: $(x - 5)(x + 5)(5x + 3) = 0$. The solutions are $x = 5, x = -5, x = -\frac{3}{5}$.

Question 19

Use the graph of the polynomial function f(x) to solve f( $$f ( x ) \text { to solve } f ( x ) = 0$$
-
A) $1,2,3$
B) $- 3 , - 1,2$
C) $- 2,1,3$
D) $- 3,2$

Accepted Answer

The answer of Use the graph of the polynomial function...

Question 20

Use the graph of the polynomial function f(x) to solve f( $$f ( x ) \text { to solve } f ( x ) = 0$$
-
A) $- 2,1$
B) $- 2,1,8$
C) $- 1,2$
D) $- 2,0,1$

Accepted Answer

The answer of Use the graph of the polynomial function...

Quiz 6: Higher-Degree Polynomial and Rational Functions

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) 0,2 B) - 2 C) - 2,0 D) 0$

Use factoring and the root method to solve the polynomial equation. - $0.1 \mathrm { x } ^ { 3 } - 9 \mathrm { x } = 0$

Solve the polynomial equation by using the root method. - $4 x ^ { 3 } - 108 = 0$

Use factoring by grouping to solve the equation. - $2 x ^ { 3 } + 8 x ^ { 2 } - 8 x - 32 = 0$

Use factoring and the root method to solve the polynomial equation. - $x ^ { 4 } - 6 x ^ { 2 } + 9 = 0$

Solve the polynomial equation by using the root method. - $\frac { 1 } { 2 } x ^ { 3 } + 4 = 0$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) - 2 , \frac { 1 } { 2 } , 3 B) - 2,3 C) - 3,2 D) - 3 , - \frac { 1 } { 2 } , 2$

Use factoring by grouping to solve the equation. - $x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32 = 0$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) - 6 , - 2,4 B) 2,4 C) - 6 , - 2 D) - 4,2,6$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) - 3,2,4 B) - 3 , - 1,2,4 C) - 4 , - 2,3 D) - 4 , - 2,1,3$

Use factoring and the root method to solve the polynomial equation. - $11 x ^ { 4 } - 33 x ^ { 2 } = 0$

$6 x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } = 0$

Solve the polynomial equation by using the root method. - $3 x ^ { 4 } - 768 = 0$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) - 4 , - 1,1,4 B) - 3 , - 1 C) - 3 , - 1,1,3 D) 1,3$

Solve the polynomial equation by using the root method. - $\frac { 1 } { 5 } x ^ { 4 } - 125 = 0$

$x ^ { 4 } - 18 x ^ { 2 } + 32 = 0$

Use factoring by grouping to solve the equation. - $5 x ^ { 3 } + 3 x ^ { 2 } - 125 x - 75 = 0$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) 1,2,3 B) - 3 , - 1,2 C) - 2,1,3 D) - 3,2$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) - 2,1 B) - 2,1,8 C) - 1,2 D) - 2,0,1$

Quiz 6: Higher-Degree Polynomial and Rational Functions

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x) =0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x) =0 -

Use factoring and the root method to solve the polynomial equation. - 0.1x3−9x=00.1 \mathrm { x } ^ { 3 } - 9 \mathrm { x } = 00.1x3−9x=0

Solve the polynomial equation by using the root method. - 4x3−108=04 x ^ { 3 } - 108 = 04x3−108=0

Use factoring by grouping to solve the equation. - 2x3+8x2−8x−32=02 x ^ { 3 } + 8 x ^ { 2 } - 8 x - 32 = 02x3+8x2−8x−32=0

Use factoring and the root method to solve the polynomial equation. - x4−6x2+9=0x ^ { 4 } - 6 x ^ { 2 } + 9 = 0x4−6x2+9=0

Solve the polynomial equation by using the root method. - 12x3+4=0\frac { 1 } { 2 } x ^ { 3 } + 4 = 021​x3+4=0

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x) =0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x) =0 -

Use factoring by grouping to solve the equation. - x3+2x2−16x−32=0x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32 = 0x3+2x2−16x−32=0

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x) =0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x) =0 -

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x) =0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x) =0 -

Use factoring and the root method to solve the polynomial equation. - 11x4−33x2=011 x ^ { 4 } - 33 x ^ { 2 } = 011x4−33x2=0

6x4+12x3+6x2=06 x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } = 06x4+12x3+6x2=0

Solve the polynomial equation by using the root method. - 3x4−768=03 x ^ { 4 } - 768 = 03x4−768=0

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x) =0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x) =0 -

Solve the polynomial equation by using the root method. - 15x4−125=0\frac { 1 } { 5 } x ^ { 4 } - 125 = 051​x4−125=0

x4−18x2+32=0x ^ { 4 } - 18 x ^ { 2 } + 32 = 0x4−18x2+32=0

Use factoring by grouping to solve the equation. - 5x3+3x2−125x−75=05 x ^ { 3 } + 3 x ^ { 2 } - 125 x - 75 = 05x3+3x2−125x−75=0

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x) =0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x) =0 -

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x) =0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x) =0 -

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) 0,2 B) - 2 C) - 2,0 D) 0$

Use factoring and the root method to solve the polynomial equation. - $0.1 \mathrm { x } ^ { 3 } - 9 \mathrm { x } = 0$

Solve the polynomial equation by using the root method. - $4 x ^ { 3 } - 108 = 0$

Use factoring by grouping to solve the equation. - $2 x ^ { 3 } + 8 x ^ { 2 } - 8 x - 32 = 0$

Use factoring and the root method to solve the polynomial equation. - $x ^ { 4 } - 6 x ^ { 2 } + 9 = 0$

Solve the polynomial equation by using the root method. - $\frac { 1 } { 2 } x ^ { 3 } + 4 = 0$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) - 2 , \frac { 1 } { 2 } , 3 B) - 2,3 C) - 3,2 D) - 3 , - \frac { 1 } { 2 } , 2$

Use factoring by grouping to solve the equation. - $x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32 = 0$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) - 6 , - 2,4 B) 2,4 C) - 6 , - 2 D) - 4,2,6$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) - 3,2,4 B) - 3 , - 1,2,4 C) - 4 , - 2,3 D) - 4 , - 2,1,3$

Use factoring and the root method to solve the polynomial equation. - $11 x ^ { 4 } - 33 x ^ { 2 } = 0$

$6 x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } = 0$

Solve the polynomial equation by using the root method. - $3 x ^ { 4 } - 768 = 0$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) - 4 , - 1,1,4 B) - 3 , - 1 C) - 3 , - 1,1,3 D) 1,3$

Solve the polynomial equation by using the root method. - $\frac { 1 } { 5 } x ^ { 4 } - 125 = 0$

$x ^ { 4 } - 18 x ^ { 2 } + 32 = 0$

Use factoring by grouping to solve the equation. - $5 x ^ { 3 } + 3 x ^ { 2 } - 125 x - 75 = 0$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) 1,2,3 B) - 3 , - 1,2 C) - 2,1,3 D) - 3,2$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 - A) - 2,1 B) - 2,1,8 C) - 1,2 D) - 2,0,1$