Question

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around at each zero. f(x) = -8(x-4)(x+1)$^3$ Determine the zero(s). The zero(s) is/are 4, -1. (Type integers or decimals. Use a comma to separate answers as needed.) Determine the multiplicities of the zero(s). Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. There is one zero. The multiplicity of the zero is (Simplify your answer.) B. There are two zeros. The multiplicity of the largest zero is . The multiplicity of the smallest zero is (Simplify your answers.) C. There are three zeros. The multiplicity of the largest zero is . The multiplicity of the smallest zero is . The multiplicity of the other zero is (Simplify your answers.)

          Find the zeros for the polynomial function and give the multiplicity for each zero.
State whether the graph crosses the x-axis or touches the x-axis and turns around at
each zero.
f(x) = -8(x-4)(x+1)$^3$
Determine the zero(s).
The zero(s) is/are 4, -1.
(Type integers or decimals. Use a comma to separate answers as needed.)
Determine the multiplicities of the zero(s). Select the correct choice below and,
if necessary, fill in the answer box(es) within your choice.
A. There is one zero. The multiplicity of the zero is 
(Simplify your answer.)
B. There are two zeros. The multiplicity of the largest zero is  . The
multiplicity of the smallest zero is 
(Simplify your answers.)
C. There are three zeros. The multiplicity of the largest zero is  . The
multiplicity of the smallest zero is  . The multiplicity of the other zero is 
(Simplify your answers.)

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Find the zeros for the polynomial function and give the multiplicity for each zero.
State whether the graph crosses the x-axis or touches the x-axis and turns around at
each zero.
f(x) = -8(x-4)(x+1)^3
Determine the zero(s).
The zero(s) is/are 4, -1.
(Type integers or decimals. Use a comma to separate answers as needed.)
Determine the multiplicities of the zero(s). Select the correct choice below and,
if necessary, fill in the answer box(es) within your choice.
A. There is one zero. The multiplicity of the zero is
(Simplify your answer.)
B. There are two zeros. The multiplicity of the largest zero is . The
multiplicity of the smallest zero is
(Simplify your answers.)
C. There are three zeros. The multiplicity of the largest zero is . The
multiplicity of the smallest zero is . The multiplicity of the other zero is
(Simplify your answers.)

Added by M-Nica T.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Kumareshwaran Rathinasabapathy

02/13/2022

Step 1

To find the zeros, we set $f(x) = 0$: $-8(x-4)(x+1)^3 = 0$ This gives us two zeros: $x-4 = 0 \implies x = 4$ and $x+1 = 0 \implies x = -1$. Show more…

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Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around at each zero. $f(x) = -8(x-4)(x+1)^3$ Determine the zero(s). The zero(s) is/are 4, -1. (Type integers or decimals. Use a comma to separate answers as needed.) Determine the multiplicities of the zero(s). Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. There is one zero. The multiplicity of the zero is $\boxed{ }$. (Simplify your answer.) B. There are two zeros. The multiplicity of the largest zero is $\boxed{ }$. The multiplicity of the smallest zero is $\boxed{ }$. (Simplify your answers.) C. There are three zeros. The multiplicity of the largest zero is $\boxed{ }$. The multiplicity of the smallest zero is $\boxed{ }$. The multiplicity of the other zero is $\boxed{ }$. (Simplify your answers.)

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Transcript

00:01 Let's determine the zeros of this function, f of x equals minus 9 times of x minus 7 times of x plus 7 raised to the power of 3.

00:09 So to determine the zeros, we have to replace f of x equals 0 and solve for x.

00:16 So we put f of x equals 0.

00:21 I'm going to replace f of x equals 0 in this function.

00:25 So we get 0 equals negative 9 times of x minus 6.

00:32 Times of x plus 7 raised to the power of 3 we can divide by negative 9 on both sides so 0 by negative 9 and this equals negative 9 over negative 9 we get x minus 6 times of x plus 7 raised to the power of 3 so 0 by negative 9 is once again 0 and negative 9 by negative 9 this equals 1 so it's basically 1 times of this expression which is x minus 6 times of x plus 7 quantity cube.

01:09 Now one of them is 0, that is either x minus 6 is 0 or we will have x plus 7 quantity cube.

01:22 This equals 0 because this is a product of two linear terms.

01:27 So either one can be 0.

01:28 When we solve this expression x minus 6 equals 0, we get x equal to 6.

01:34 And similarly, we can solve this expression or the equation x plus 7 quantity cube equal to 0 by taking cube root on both sides.

01:43 So when we do that, we get x plus 7 equals 0 because cube root of 0 is 0.

01:49 Now we solve for x, that is x equal to negative 7.

01:53 And since we are taking a cube root to solve this x, we will have a multiplicity of 3 for this negative 7.

02:02 So we say that this is with multiplicity 3.

02:06 So these are the zeros of this function.

02:10 So we say that the zeros of this function are 6 and minus 7.

02:16 And this minus 7 is with multiplicity 3.

02:24 Let's choose the correct choice given below...

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