Algebra, equations, and inequalities - Intro to Algebra

15 important questions on Algebra, equations, and inequalities - Intro to Algebra

What is a variable (how is it defined)?

A letter that represents either a specific number or all numbers.

What is a constant (how is it defined)?

A number or a symbol (like pi) that does not change in value (hence its name).

What is a term (how is it defined)?

A product of constants and variables including powers of variables.
  • Higher grades + faster learning
  • Never study anything twice
  • 100% sure, 100% understanding
Discover Study Smart

What is a coefficient (how is it defined)?

The constant factor of a term. For example in: 6y^2, 6 is the coefficient.

Do expressions have equal signs why or why not?

No (explanation still to follow see vidoe lesson 3.37).

How do monomials, binomials, trinomials and polynomials differ/relate to each other?

These are expressions with its name based on the number of terms it has:
Monomial: expression with exactly 1 term.
Binomial: expression with exactly 2 terms.
Trinomial: expression with exactly 3 terms.
Polynomial: expression with any number of terms involving only one variable.

Of the following 2 expressions, explain why either is a polynomial or not.
Expression 1: x^2 + 4x - 21
Expression 2: a^2 + b^2 -c^2

First of all, both are examples of trinomials (expressions with exactly 3 terms).
But only the first is an example of a polynomial because a polynomial has only 1 variable (first expression's variable: x).

The 2nd expression has 3 variables.

What is a linear term (example)?

2x is an example of a linear term (no explicitly written exponent)

What is an example of a quadratic term?

5x^2 is an example of a quadratic term (a term with the square of a single variable).

What is an example of a cubic term?

2x^3 is an example of a cubic term (a term with the cube of a single variable).

Identify the following expression: 17x (make sure you understand why).

Linear monomial

Identify the following expression: 14x^2 (make sure you understand why).

Quadratic monomial

Identify the following expression: 2x^2 + 8x
(make sure you understand why).

Quadratic binomial with a quadratic term (2x^2) and a linear term (8x)

Identify the following expression: x2 - 10x + 25 (make sure you understand why).

Is a quadratic trinomial with a quadratic term (x2), a linear term (-10x) and a constant term (25).

Please identify the coefficient of the linear term of this expression: x2 - 10x + 25

The linear term is: -10x and the coeefficient here is -10.

The question on the page originate from the summary of the following study material:

  • A unique study and practice tool
  • Never study anything twice again
  • Get the grades you hope for
  • 100% sure, 100% understanding
Remember faster, study better. Scientifically proven.
Trustpilot Logo