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Answer:

x³ + 10x² + 1

Step-by-step explanation:

To rewrite the given polynomial in standard form, we need to arrange the terms in descending order of the exponent of the variable. The standard form of a polynomial is the form where the terms are written from highest to lowest degree.

The given polynomial is:

10x² + 1 - x³

To rewrite it in standard form, we first rearrange the terms in descending order of the exponent:

∴ x³ + 10x² + 1

Now the polynomial is in standard form.

Additional Information:

Polynomial: A polynomial is a mathematical expression that consists of variables (like x), coefficients (numbers), and non-negative integer exponents. The standard form of a polynomial is written with the terms in descending order of the exponents.

Degree of a polynomial: The degree of a polynomial is the highest exponent of the variable in that polynomial. In the given polynomial, the term with the highest degree is -x^3, so the degree of the polynomial is 3.

Exponent: The exponent of a term indicates the number of times the variable is multiplied by itself. For example, x^3 means x · x · x.

Coefficient: The coefficient is the number that multiplies the variable in each term. For example, in the term 10x^2, the coefficient is 10.

Descending order: When arranging the terms of a polynomial in descending order, we write the term with the highest degree first, followed by the term with the second-highest degree, and so on, until we reach the constant term (a term without a variable).

In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct  random sampling and random group assignment

Explanation:

The terms Random sampling and Random group assignment are greatly different in process of the sample selection.  The study related to the determination of how sample participants can be drawn from the population refers to the process of Random sampling. The sample participants are subjected to a treatment by the usage of a random procedure comprises the Random group assignment.

When a researcher wants validate externally then random selection can be used. When a researcher wants to determine the effects of treatment within that group which is known as determination of internal validity then he can opt for Random group assignment.

Answer:

In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.

Explanation:

Random selection is a representation of the sample of people for your research from a community. Random assignment is the assigning of the sample that describes various groups or operations in the study.

Reasons:

• Random sampling enables us to get a sample representative of the community.
• Random assignment enables us to make positive that the only distinction among the various treatment combinations is what needs to study.

• Random assignment is crucial for sound empirical design. With adequately large representations, random assignment performs it unlikely that there are methodical variations among the groups.

Thus we can say in order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.

To learn more about random sampling/random group assignment, refer:

• brainly.com/question/9423006

Answer: The remainder when f(x) is divided by (x-2) is 217.

Step-by-step explanation:

Since we have given that

And it is divided by g(x)=(x-k)

Here, k= 2

So, g(x)= x-2

So, we need to find the remainder .

By using "Remainder theorem ":

Now,

Hence, the remainder when f(x) is divided by (x-2) is 217.

It is to be solved by reminder thorem
f(x)/(x-k) will have reminder f(k), 
so, f(2) = 5*(2^4) + 8 *(2^3) +4* (2^2) -5(2) +67

             =5*16 + 8*8 +4*4 -5*2 +67
             =80 + 64 + 16 -10 +67

             = 217