Classifying Polynomial Expressions and Identifying Terms, Coefficients, and Constants

Math Problem Statement

Identify the parts of each algebraic expressions by completing the table.

a. −푏푐

+2푑+9

Coefficients

Variables

Constant

Terms

Classify

b. 3푥

+4푦

−푧+11

Coefficients

Variables

Constant

Terms

Classify

Let's analyze the two algebraic expressions and break them down according to the requested categories.

$-\frac{bc}{2} + 2d + 9$

Category	Expression a
Coefficients	-1/2 (for $bc$ ), 2 (for $d$ )
Variables	$b$ , $c$ , $d$
Constant	9
Terms	$-\frac{bc}{2}$ , $2d$ , 9
Classify	Trinomial (since there are three terms)

$3x^2 + 4y^3 - z + 11$

Category	Expression b
Coefficients	3 (for $x^2$ ), 4 (for $y^3$ ), -1 (for $z$ )
Variables	$x$ , $y$ , $z$
Constant	11
Terms	$3x^2$ , $4y^3$ , $-z$ , 11
Classify	Polynomial with four terms (also known as a quadrinomial)

Do you need further clarification on any part of this analysis?

Here are 5 related questions for deeper understanding:

Tip: In algebraic expressions, the degree of a term is the sum of the exponents of the variables in that term.

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