Question

polynomial monomial identify - circle your final answer 1. $4x + 37y + 5$ how many terms?_ what are the variables?_ what is the coefficients_ 3. $12 + 5p^{2}+23k$ how many terms?_ what are the variables?_ what is the coefficients_ 2. $3p + 378y^{7}-34 + 9k$ how many terms?_ what are the variables?_ what is the coefficient of the $1^{st}$ term?_ 4. $4a + 37b + 5c - 21$ how many terms?_ what are the variables?_ what is the coefficient of the $3^{rd}$ term_

Explanation:

Step1: Count terms in \(3p + 378y^{7}-34 + 9k\)

A term is a single number, variable, or product of numbers and variables. Here, \(3p\), \(378y^{7}\), \(-34\), \(9k\) are terms. So, number of terms \( = 4\).

Step2: Identify variables in \(3p + 378y^{7}-34 + 9k\)

Variables are symbols that represent unknown values. Here, \(p\), \(y\), \(k\) are variables.

Step3: Find coefficient of \(1^{st}\) term in \(3p + 378y^{7}-34 + 9k\)

The coefficient is the numerical factor of a term. For the term \(3p\), the coefficient is \(3\).

Step4: Count terms in \(4a + 37b + 5c-21\)

The terms are \(4a\), \(37b\), \(5c\), \(-21\). So, number of terms \( = 4\).

Step5: Identify variables in \(4a + 37b + 5c-21\)

The variables are \(a\), \(b\), \(c\).

Step6: Find coefficient of \(3^{rd}\) term in \(4a + 37b + 5c-21\)

The \(3^{rd}\) term is \(5c\), and its coefficient is \(5\).

Answer:

1. How many terms? \(4\); What are the variables? \(p,y,k\); What is the coefficient of the \(1^{st}\) term? \(3\)
2. How many terms? \(4\); What are the variables? \(a,b,c\); What is the coefficient of the \(3^{rd}\) term? \(5\)