To find the order of the expression, first define what the order of an expression represents.

In a general example,

\(\displaystyle ax^n\)

\(\displaystyle a\) represents the coefficient of the \(\displaystyle x\) term and \(\displaystyle n\) represents the degree or order of the expression.

When there are more than one term in an expression such as,

\(\displaystyle x^2+y^3+xy^3\)

the order of that expression is the highest degree on a given term.

In mathematical terms, 

\(\displaystyle \\x^2\rightarrow \text{Degree}=2 \\y^3\rightarrow \text{Degree}=3 \\xy^3\rightarrow \text{Degree}=1+3=4\)

therefore the order of the expression is four.

Looking at the specific expression in question the following is seen.

\(\displaystyle 2x^2+xy+y^3\)

\(\displaystyle \\2x^2\rightarrow \text{Degree}=2 \\xy\rightarrow \text{Degree}=1+1=2 \\y^3\rightarrow \text{Degree}=3\)

Therefore, the order of the expression is three.

To find the coefficient on the \(\displaystyle x\) term, first define what the coefficient of an expression represents.

In a general example,

\(\displaystyle ax^n\)

\(\displaystyle a\) represents the coefficient of the \(\displaystyle x\) term and \(\displaystyle n\) represents the degree or order of the expression.

For the particular expression in this question,

\(\displaystyle y^2+3x\)

the \(\displaystyle x\) term is \(\displaystyle 3x\).

Therefore the \(\displaystyle a\) value or coefficient is,

\(\displaystyle 3x\rightarrow a=3\)

To find the terms of the expression, first define what a term represents.

In a general example,

\(\displaystyle ax^n\)

\(\displaystyle a\) represents the coefficient of the \(\displaystyle x\) term and \(\displaystyle n\) represents the degree or order of the expression. The term in this case is \(\displaystyle ax^n\).

When there are more than one term in an expression such as,

\(\displaystyle x^2+y^3+xy^3\)

each term is separated by an algebraic operation such as an addition or subtraction sign.

In the given expression,

\(\displaystyle 3x^2-y+4x\)

there are three terms,

\(\displaystyle \\\text{Term One}=3x^2 \\\text{Term Two}=y \\\text{Term Three}=4x\)

Looking at the possible answer choices,

\(\displaystyle 3x^2\) matches a term in the expression. 

\(\displaystyle 4\) represents the coefficient on the \(\displaystyle x\) term but does not represent a term itself.

\(\displaystyle 4x+y\) is an expression with two terms. 

\(\displaystyle 1\) is an integer.

\(\displaystyle +\) is the addition operation sign that separates terms.

Expressions can be written in both English terms and mathematical terms. This particular question is giving the English version of an expression and is asking for the mathematical version.

To convert this expression into the mathematical version, identify key words that represent algebraic operations.

For example,

"A number" means a variable such as \(\displaystyle x\), \(\displaystyle y\), and others.

"Sum, more than, in addition to" means addition \(\displaystyle +\).

"Difference, less than" means subtraction.

"Times, multiple of" means multiplication.

Break down the English sentence and identify the mathematical expression.

"Two more than four times a number" 

"Two more" means: \(\displaystyle +2\)

"Four times a number" means: \(\displaystyle 4x\)

Combine the terms into one expression, 

\(\displaystyle 4x+2\)

Factors of a term are the parts that make up that term. 

For example,

\(\displaystyle 6=2\cdot 3\)

\(\displaystyle x^2=x\cdot x\)

Breaking down the term in question is as follows.

\(\displaystyle 8x\)

The coefficient eight can be broken down into its factors,

\(\displaystyle 8\rightarrow2\cdot 4\rightarrow 2\cdot 2\cdot 2\)

and the variable term cannot be broken down any further.

\(\displaystyle x\rightarrow x\cdot 1\)

Therefore, the factors of \(\displaystyle 8x\) are \(\displaystyle 2\cdot2\cdot2\cdot x\).

To find the order of the expression, first define what the order of an expression represents.

In a general example,

\(\displaystyle ax^n\)

\(\displaystyle a\) represents the coefficient of the \(\displaystyle x\) term and \(\displaystyle n\) represents the degree or order of the expression.

When there are more than one term in an expression such as,

\(\displaystyle x^2+y^3+xy^3\)

the order of that expression is the highest degree on a given term.

In mathematical terms, 

\(\displaystyle \\x^2\rightarrow \text{Degree}=2 \\y^3\rightarrow \text{Degree}=3 \\xy^3\rightarrow \text{Degree}=1+3=4\)

therefore the order of the expression is four.

Looking at the specific expression in question the following is seen.

\(\displaystyle 2x^2+xy\)

\(\displaystyle \\2x^2\rightarrow \text{Degree}=2 \\xy\rightarrow \text{Degree}=1+1=2\)

Therefore, the order of the expression is two.

To find the coefficient on the \(\displaystyle x\) term, first define what the coefficient of an expression represents.

In a general example,

\(\displaystyle ax^n\)

\(\displaystyle a\) represents the coefficient of the \(\displaystyle x\) term and \(\displaystyle n\) represents the degree or order of the expression.

For the particular expression in this question,

\(\displaystyle y^2+3x\)

the \(\displaystyle y\) term is \(\displaystyle y^2\).

Therefore the \(\displaystyle a\) value or coefficient is,

\(\displaystyle y^2\rightarrow a=1\)

To find the terms of the expression, first define what a term represents.

In a general example,

\(\displaystyle ax^n\)

\(\displaystyle a\) represents the coefficient of the \(\displaystyle x\) term and \(\displaystyle n\) represents the degree or order of the expression. The term in this case is \(\displaystyle ax^n\).

When there are more than one term in an expression such as,

\(\displaystyle x^2+y^3+xy^3\)

each term is separated by an algebraic operation such as an addition or subtraction sign.

In the given expression,

\(\displaystyle 2x^2+4y+1x\)

there are three terms,

\(\displaystyle \\\text{Term One}=2x^2 \\\text{Term Two}=4y \\\text{Term Three}=1x\)

Looking at the possible answer choices,

\(\displaystyle 2x^2\) matches a term in the expression. 

\(\displaystyle 4\) represents the coefficient on the \(\displaystyle x\) term but does not represent a term itself.

\(\displaystyle 4x+y\) is an expression with two terms. 

\(\displaystyle 1\) is an integer.

\(\displaystyle +\) is the addition operation sign that separates terms

Expressions can be written in both English terms and mathematical terms. This particular question is giving the English version of an expression and is asking for the mathematical version.

To convert this expression into the mathematical version, identify key words that represent algebraic operations.

For example,

"A number" means a variable such as \(\displaystyle x\), \(\displaystyle y\), and others.

"Sum, more than, in addition to" means addition \(\displaystyle +\).

"Difference, less than" means subtraction.

"Times, multiple of" means multiplication.

Break down the English sentence and identify the mathematical expression.

"Two less than three times a number" 

"Two less" means: \(\displaystyle -2\)

"Three times a number" means: \(\displaystyle 3x\)

Combine the terms into one expression, 

\(\displaystyle 3x-2\)

Factors of a term are the parts that make up that term. 

For example,

\(\displaystyle 6=2\cdot 3\)

\(\displaystyle x^2=x\cdot x\)

Breaking down the term in question is as follows.

\(\displaystyle 3x^2\)

The coefficient three cannot be broken down,

\(\displaystyle 3\rightarrow1\cdot 3\)

and the variable term can be broken down into its factors.

\(\displaystyle x^2\rightarrow x\cdot x\)

Therefore, the factors of \(\displaystyle 3x^2\) are \(\displaystyle 3\cdot x\cdot x\).