Question

identify the kind of algebraic expression and determine the degree, variables and constant
3abc2+a2bc2-abc+2

Answer 1

SOLUTION

TO DETERMINE

To identify the kind of algebraic expression and determine the degree, variables and constant in

$\sf{3ab {c}^{2} + {a}^{2} b {c}^{2} - abc + 2 }$

CONCEPT TO BE IMPLEMENTED

POLYNOMIAL

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

Polynomials have no variables in denominators or exponents, no roots or absolute values of variables, and all variables have whole number exponents

EVALUATION

Here the given expression is

$\sf{3ab {c}^{2} + {a}^{2} b {c}^{2} - abc + 2 }$

Since there are four terms in the expression, so it is a four term polynomial

Now in the given polynomial there are more than one variable, we need to find the degree by adding the exponents of each variable in each term.

Here the middle term in the expression

$\sf{ {a}^{2} b {c}^{2} }$

So the degree of the polynomial

= 2 + 1 + 2

= 5

Here the variables are a , b , c

Also the Constant term = 2

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Answer 2

$\huge\ \underline \mathbb{\color{red}{SOLUTION}}$

$\bf \underline {\color{orange}{TO \: \: DETERMINE : }}$

To identify the kind of algebraic expression and determine the degree, variables and constant in

$\sf{\color{teal}{3ab {c}^{2} + {a}^{2} b {c}^{2} - abc + 2}}$

$\bf \underline{ \color{deepskyblue}{CONCEPT  \: TO \: BE \:  IMPLEMENTED}}$

$\bf\underline{\color{midnightblue}{POLYNOMIAL:}}$

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables.

$\bf \underline{ \purple{DEGREE \: OF \:A\:POLYNOMIAL : }}$

Degree of a polynomial is defined as the highest power of its variable that appears with non zero coefficient.

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

Polynomials have no variables in denominators or exponents, no roots or absolute values of variables, and all variables have whole number exponents.

$\bf \underline{ \color{green}{EVALUATION : }}$

Here the given expression is

$\sf{\color{royalblue}{3ab {c}^{2} + {a}^{2} b {c}^{2} - abc + 2 }}$

Since there are four terms in the expression, so it is a four term polynomial.

Now in the given polynomial there are more than one variable, we need to find the degree by adding the exponents of each variable in each term.

Here the middle term in the expression

$\sf{\color{chocolate}{ {a}^{2} b {c}^{2} }}$

So the degree of the polynomial

= 2 + 1 + 2

= 5

$\sf{ \pink {Here \: the \: variables \: are \: a , b , c}}$

$\sf{ \color{blue}{Also \: the \: Constant \: term = 2}}$

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