1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ivahew [28]
1 year ago
5

3. For the polynomial: ()=−2(+19)3(−14)(+3)2, do the following:A. Create a table of values that have the x-intercepts of p(x) in

the first column and their multiplicities in the second column.B. State the degree and end behavior for p(x). C. Hand sketch a rough graph of p(x). You should have the x-int labeled, but you do not need tick marks for all numbers in between.
Mathematics
1 answer:
Pepsi [2]1 year ago
6 0

Part A. We are given the following polynomial:

\mleft(\mright)=-2\mleft(+19\mright)^3\mleft(-14\mright)\mleft(+3\mright)^2

This is a polynomial of the form:

p=k(x-a)^b(x-c)^d\ldots(x-e)^f

The x-intercepts are the numbers that make the polynomial zero, that is:

\begin{gathered} p=0 \\ (x-a)^b(x-c)^d\ldots(x-e)^f=0 \end{gathered}

The values of x are then found by setting each factor to zero:

\begin{gathered} (x-a)=0 \\ (x-c)=0 \\ \text{.} \\ \text{.} \\ (x-e)=0 \end{gathered}

Therefore, this values are:

\begin{gathered} x=a \\ x=c \\ \text{.} \\ \text{.} \\ x=e \end{gathered}

In this case, the x-intercepts are:

\begin{gathered} x=-19 \\ x=14 \\ x=-3 \end{gathered}

The multiplicity are the exponents of the factor where we got the x-intercept, therefore, the multiplicities are:

Part B. The degree of a polynomial is the sum of its multiplicities, therefore, the degree in this case is:

\begin{gathered} n=3+1+2 \\ n=6 \end{gathered}

To determine the end behavior of the polynomial we need to know the sign of the leading coefficient that is, the sign of the coefficient of the term with the highest power. In this case, the leading coefficient is -2, since the degree of the polynomial is an even number this means that both ends are down. If the leading coefficient were a positive number then both ends would go up. In the case that the leading coefficient was positive and the degree and odd number then the left end would be down and the right end would be up, and if the leading coefficient were a negative number and the degree an odd number then the left end would be up and the right end would be down.

Part C. A sketch of the graph is the following:

If the multiplicity is an odd number the graph will cross the x-axis at that x-intercept and if the multiplicity is an even number it will tangent to the x-axis at that x-intercept.

You might be interested in
Solve for x. 5x=15+5
Travka [436]

Answer: x=4

Step-by-step explanation:

5x=15+5

15+5=20

5x=20

divide 5 on both sides

20/5=4

x=4

6 0
3 years ago
Read 2 more answers
Choose all that define a rectangle in the coordinate plane by the four given points.
inysia [295]

Answer:

The answer is A(-3,-4) B(-1,2) C(2,1) D(0,-5)

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Given right triangle ABC with right angle C, and sin A = ¼. Which of the following expressions are also equal to ¼?
BaLLatris [955]

Answer:

cos(A)

Step-by-step explanation:

5 0
2 years ago
4+b = -30<br> What is the value of X?<br><br> X= -34<br> X= 7.5 <br> X=120<br> X= -26
Firdavs [7]

Answer:

X= -34

Step-by-step explanation:

6 0
3 years ago
What do I do to figure out this problem:<br>3x+8=26+x
Gnom [1K]
<span><u>3x + 8 = 26 + x</u>

The first thing you need to do is understand what you're looking for ...
what a 'solution' means, what it looks like, and how you even know
when you have it.    I'm not sure you're there yet.

The 'answer' or the 'solution' to the problem is a number.  It's the number
that 'x' must be in order for that line at the top to be a true statement.  There's
only one possibility.

To find it, you can do anything you want to either side of the problem, as long as
you do exactly the same thing to the other side too.  With that ability, here's how
to 'figure out the problem', and find the answer:

The original problem:      </span><span><u>3x + 8 = 26 + x</u>

Subtract 8 from each side:

3x = 18 + x

Subtract 'x' from each side:

2x = 18

Divide each side by 2 :

<u>x = 9 </u> .

That's what the answer looks like, and that's what the answer is.

' 9 ' is the ONLY number you can write in place of 'x' in the problem,
and have the problem read true.

I'll show you what I mean.  Let's take the original problem

                   </span><span> <u><span>3x + 8 = 26 + x

</span></u><span>and let's write ' 2 ' wherever we see 'x' :

3 (2) + 8 = 26 + 2

3 (2) means 3 times 2, and that's 6 .
So now we have

6 + 8 = 26 + 2

Do the addition on each side, and we have

14 = 28 .

That's nonsense.  14 is not equal to 28 .  The reason that happened
is because we put the wrong number in place of 'x' .  When we put the
correct number in place of 'x', the left side will be equal to the right side.
To 'figure out the problem' means to find out what that number must be.
For this particular problem, it's 9 .
</span><u><span /></u>

</span>

7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the length of fathoms shadow?
    10·1 answer
  • What is 4.95 as a fraction
    5·2 answers
  • PLEASE HELP!
    12·1 answer
  • Hello can you please help me posted picture of question
    13·1 answer
  • in July ,gas price increse by 15%. in agust , they decrease by 10%. what is the total percent change since june
    5·1 answer
  • What is -3x6 with explanation
    8·2 answers
  • What is cos K? I suck at math:(
    10·1 answer
  • The circumference of a circle is 32 centimeters. Which is closest to the radius? A. 10.2 centimeters B. 5.1 centimeters C. 16 ce
    11·2 answers
  • Coficient of x^2 in -4x^2
    10·1 answer
  • PLZ HELP ME! THIS IS A GRADE! NO LINKS!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!