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2 years ago

The Remainder Theorem can be used as a shortcut to find the remainder when a function is divided by a binomial.

1 answer:

6 0

The Remainder Theorem is used to determine whether a linear binomial is a factor of a polynomial because it helps us factorize the polynomial more easily.

<h3>How to illustrate the theorem?</h3>

The remainder theorem states that if P(x) is a polynomial and x - a is a linear factor, the remainder when P(x) is divided by x - a is P(a). When P(a) = 0, then x - a is a factor of P(x).

Here, the remainder theorem is used to determine whether a linear binomial is a factor of a polynomial because it helps us factorize the polynomial more easily.

When the polynomial is divided by the linear factor, we obtain a polynomial of a lesser degree which can then be further factorized to obtain all the factors of our initial polynomial.

A linear binomial is the factor of a polynomial if the polynomial value is 0 at the zeros of the linear binomial

Let's assume a polynomial function is

P(x) = (x - 3)(x + 1)(x -2)

And a linear binomial is:

x - 3 = 0

We start by calculating the value of x in x - 3 = 0

x = 3

Next, we substitute x = 3 in P(x) = (x - 3)(x + 1)(x -2)

P(3) = (3 - 3)(3 + 1)(3 -2)

Evaluate

P(3) = 0

Since P(3) = 0, then the linear binomial x - 3 is a factor of P(x) = (x - 3)(x + 1)(x -2)

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You might be interested in

An automobile dealer had 288 cars and trucks in stock during the month. He must pay an inventory fee of 52 per car and $5 per tr

Aleonysh [2.5K]

For the given conditions, we won’t get a practical solution.

<u>Solution:</u>

Given, An automobile dealer had 288 cars and trucks in stock during the month.

He must pay an inventory fee of 52 per car and $5 per truck.

He paid $849 for inventory foes.

We have to find how many cars and Trucks did he have during the month?

Now, let the number of trucks be n, then number of cars will be 288 – n

And, according to given information,

$\begin{array}{l}{5 \times n+52 \times(288-n)=849} \\\\ {\rightarrow 5 n+52 \times 288-52 n=849} \\\\ {\rightarrow 52 n-5 n=14976-849} \\\\ {\rightarrow 47 n=14127} \\\\ {\rightarrow n=300.57}\end{array}$

Here we got n > number of cars and trucks, which is practically impossible.

Hence, for the given conditions, we won’t get a practical solution

8 0

3 years ago

Difference of Squares gives which complex factors for the expression x² +11?

77julia77 [94]

Answer:

Step-by-step explanation:

Discussion

i has to appear somewhere. That lets D and B out. They are both wrong.

C has only one i. It can't be right either. You need 2 i-s which will multiply to +1 when squared. That leaves you with a.

The way a is written, it can't be the answer either. For one thing, that 2 makes the answer question at best.

I would say there is no correct answer. Could you check the question? Also it would be a good idea to ask your instructor how this works, in case I'm wrong.

7 0

2 years ago

Which of these statements are true if you need to make an inference about the mean of a population?

lorasvet [3.4K]

Answer:

I. You must use a t test rather than a z-test unless you know the population standard deviation.

Correct when the population deviation is not known we can assume that the distribution follows a t distribution in order to do inferences about the population mean

II. If you do not know the population standard deviation, your sample must be a simple random sample from a normal population.

False is not required since we can use the t distribution when the sample size is not large enough and when the data is not perfectly Normal

III. Sample sizes must be at least 30.

True that ensure that the condition 2) would be satisfied.

Step-by-step explanation:

In order to make inferences about the population mean we need 4 important conditions:

1) Random: We need data from a random sample of size n out of the population of interest.

2) Normal: We need that the variable follows a Normal distribution. Sometimes we just need that the distribution would be symmetric and with a large sample.

3) Independent: We need that the population would be much larger than the sample (at least 20 or 30 times as large).

4) Standard Deviation: We need to have the population standard deviation.

Now if we analyze one by one the conditons we have:

I. You must use a t test rather than a z-test unless you know the population standard deviation.

Correct when the population deviation is not known we can assume that the distribution follows a t distribution in order to do inferences about the population mean

II. If you do not know the population standard deviation, your sample must be a simple random sample from a normal population.

False is not required since we can use the t distribution when the sample size is not large enough and when the data is not perfectly Normal

III. Sample sizes must be at least 30.

True that ensure that the condition 2) would be satisfied.

6 0

3 years ago

Zana Lovley has a small craft

Maksim231197 [3]

Answer:

$619.56

Step-by-step explanation:

Think ALOE: Assets = Liabilities + Owner's Equity (capital)

Assets- anything of value you own (+)

Add 400.25, 612.84, 58.72, 468.22

400.25 + 612.84 + 58.72 + 468.22

= 1540.03 (this is Zana's total assets and owner's equity - both sides of the aloe equation have to stay equal)

Owing someone is a liability, therefore subtract 807.58 and 112.89 from your assets and owner's equity

1540.03 - 807.58 = 732.45

732.45 - 112.89 = $619.56

Zana's capital is $619.56

Have a lovely rest of your day! :)

6 0

2 years ago

Write an expression thats is equivalent to 8(a+5)

son4ous [18]

Answer:

8a+40

Step-by-step explanation:

8(a+5)

Distribute the (8) by multiplying it by the (a) and the (5).

8 0

3 years ago