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
Natali5045456 [20]
3 years ago
15

2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap

h. please use synthetic division

Mathematics
1 answer:
telo118 [61]3 years ago
4 0

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if \frac{p}{q} is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1  10  35  50  24

  <u>| 0  -1  -9  -26   -24</u>

   <u> 1    9  26  24    0</u>

Hence quotient is x^{3} +9x^{2} +26x+24

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1   9  26   24

   <u>| 0  -2  -14   -24</u>

   <u>  1    7    12     0</u>

Hence quotient is x^{2} +7x+12

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

(-3)^{2}+7(-3)+12=-9-21+12=0

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1  7  12

   <u>| 0 -3  -12</u>

    <u> 1    4    0</u>

Hence quotient is x+4.

So, f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)

Please have a look at the graph attached.

You might be interested in
In a certain town in the united states, 40% of the population are democrats and 60% are republicans. The municipal government ha
mixer [17]

Answer:

(a) 0.48, (b) 0.625, (c) 0.1923

Step-by-step explanation:

First define

Probability a person is a democrat: P(D) = 0.4

Probability a person is a republican: P(R) = 0.6

Probability a person support the measure given that the person is a democrat: P(SM | D) = 0.75

Probability a person support the measure given that the person is a republican: P(SM | R) = 0.3

Now for the Theorem of total probabilities we have

(a) P(SM) = P(SM | D)P(D)+P(SM | R)P(R) = (0.75)(0.4)+(0.3)(0.6) = 0.48

and for the Bayes' Formula we have

(b) P(D | SM) = P(SM | D)P(D)/[P(SM | D)P(D)+P(SM | R)P(R)] = (0.75)(0.4)/0.48 = 0.625

Now let SMc be the complement of support the measure, i.e.,

P(SMc | D) = 0.25 : Probability a person does not support the measure given that the person is a democrat

P(SMc | R) = 0.7: Probability a person does not support the measure given that the person is a republican,

and also for the Bayes' Formula we have

(c) P(D | SMc) = P(SMc | D)P(D)/[P(SMc | D)P(D)+P(SMc | R)P(R)] = (0.25)(0.4)/[(0.25)(0.4)+(0.7)(0.6)] = 0.1/(0.52)=0.1923

4 0
3 years ago
The air temperature drops from 94°F to 72°F in 15 minutes what is the change in temperature
mamaluj [8]
The temperature drops 22<span>°F in 15 minutes.

22</span>°F / 15 = 1.46<span>°F per minute

Hope I helped!</span>
7 0
3 years ago
benny uses 2/5 grams (G) of toothpaste each time he brushes his teeth. If benny buys 30-g tube, how many times will be able to b
worty [1.4K]

Answer:

75

Step-by-step explanation:

First divide 2/5 to get 0.4. Then divide 30 by 0.4 to get the answer. A simple way to think about it is how many 0.4 grams are in 30 gram tube.

5 0
2 years ago
What number is 1/5 of another number the sum of the two numbers is six find the two numbers
Oliga [24]

Answer:

the two numbers are 3 and 3.

1/5 of 3 is 0.6

1/5 of 6 is 1.2

Step-by-step explanation:

3 + 3 = 6

(1/5)3 = 0.6

(1/5)6 = 1.2

8 0
2 years ago
The diagonal of a rectangle is 25 in. The width is 15 in. What is the area of the rectangle?
Nana76 [90]

Answer:

375 in² is the answer.

Step-by-step explanation:

Are of rectangle= area of 2 triangle

= 1/2*25*15+1/2*25*15

=187.5+187.5

=375 in²

7 0
2 years ago
Other questions:
  • How do I write 28,500/100,000 as a decimal number?
    14·1 answer
  • What is the simplified form of the expression? ( m^-1 m^5 / m^-2) ^-3       
    11·2 answers
  • The following sets of numbers are possible side lengths of a triangle. Which of the following sets forms a Pythagorean triple?
    15·2 answers
  • out of 400 light bulbs 16 are defective at this rate how many defective bulbs would be in a lot of 44000
    13·1 answer
  • Jackson had $25 to spend on groceries . After purchasing 5 cantaloupes he had $2.50 left how much did each cantaloupe cost
    7·1 answer
  • Decide if you are given enough information to prove that the quadrilateral is a parallelogram: one pair of consecutive angles ar
    13·2 answers
  • 14÷976= /32÷1857 show your work please help
    15·1 answer
  • Confounding
    14·1 answer
  • K + 0.10k and 1.1 k is equivalent yes or no​
    10·1 answer
  • How many lines of symmetry does this figure have​
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!