classify the expression by the number of terms PLEASE HELP ASAP

Question

14/3 x^2 yz^3

Answer 1

Here are some examples of monomials (one term):

7 (a constant term)

3x (consists of two "factors" being multiplied; 3 is a factor and x is a factor)

5x²y⁷ (still factors being multiplied although the factors of x and y have been written concisely using exponents)

Here are a few examples of binomials (two terms):

3x + 7 (3x is a term and 7 is a term; terms are separated by + or - signs)

5x²y⁷ + 3x

(6/7)x² - 3y² (that negative sign actually is the sign if the 2nd term, so the terms are (6/7)x² and -3y²)

When terms are separated by a minus sign it helps to visualize the expression like this:

5x² + (-3y) (this would normally be written 5x² - 3y, but visualize the terms separated by an invisible + sign)

The leading term also has a sign so in that last expression it is understood that the leading term is +5x².

Here are a couple trinomials (3 terms):

6x²y³ - 3z⁵ + 7km³

-5xy - 3mn + 7r⁵

No + or - signs are visible in your post so:

(14/3) x²yz³ is one term (a monomial)

That term has a constant "factor" (14/3) and additional factors that are powers of x, y, and z.

It is a common error to use the word "term" incorrectly when what is really meant is factor.

Let's say you have the following formula for the perimeter of a rectangle and are asked to solve for L:

P = 2L + 2W

The right side of that formula contains two terms. In order to isolate L picture subtracting the term +2W from both sides of the equation. (another way to think about it is that you are going to "drag" that term from the right side to the left side--to drag a term, picture moving it to the other side and changing its sign). That is why it is important to understand that every term has its own sign.

P - 2W = 2L

Finally to isolate L divide both sides by its coefficient (2) -- or multiply both sides by the reciprocal of the coefficient.

L = (P - 2W)/2 or L = (1/2)[P - 2W]

There are additional items to take into consideration when defining a term (like what about division; what about an algebraic expression in parentheses)?

(x-3)/5 - 3(2x + 7) = 4

Right now there are two terms to the left of the equal sign. If you choose to solve this equation by multiply every term by 5 to clear the equation of fractions you could get something like this:

x - 3 -15(2x + 7) = 20 (now there are three terms left of the equal sign)

x - 3 - 30x - 105 = 20 (now 4)

-29x - 108 = 20 (now 2)

-29x = 20 + 108 (the -108 has been dragged to the right of the equal sign (another word for dragged is transposed)

-29x = 128

x = -(128/29)

Hopefully these examples give some idea of how a term is defined. For more detail and practice do a search for "algebra what is a term". For example:

byjus.com/maths/expression-term-factor-coefficient/