Question

Organize the following expressions from greatest to least by number of terms:

i. x^2yz,
ii. 3xyz
iii. 2x^2y - x^2 − 3x^4
iv. 9x^2yz

options:
a. iii, i, iv, ii
b. ii, i, iii, iv
c. iii, ii, i, iv
d. i, ii, iv, iii

Answer 1

The expressions are organized based on the number of terms they contain. Expression iii has the most with 3 terms, while expressions i, ii, and iv all have 1 term each. The correct order from greatest to least is iii, i, iv, ii.

Step-by-step explanation:

To organize the expressions from the greatest to the least number of terms, we first need to identify how many terms each expression has. A term in an algebraic expression is a single mathematical entity that can be separated by a plus (+) or minus (-) sign.

• i. x^2yz has 1 term.
• ii. 3xyz has 1 term.
• iii. 2x^2y - x^2 − 3x^4 has 3 terms.
• iv. 9x^2yz has 1 term.

Thus, organizing these from the greatest to the least number of terms we have:

1. 2x^2y - x^2 − 3x^4 (iii. with 3 terms)
2. x^2yz (i. with 1 term), 3xyz (ii. with 1 term), 9x^2yz (iv. with 1 term)

So the correct answer is (a) iii, i, iv, ii.