Question

name
applying the standard
how might this standard appear on a test?

1. analyze each of the eight expressions. write each expression under the category that correctly. expressions may be written under more than one category.

8b - 4
3x² + 15x + 1
3c - 2p + 6k - 12
1
(3n)/4 + 7m
2 - (4w + 3y)
16abc + 2d
(12b)/5
contains 2 or fewer terms
2 contains 3 or more terms
contains a constant
contains more than one product
contains at least one quotient
contains more than one coefficient
(3n)/4 + 7m
(12b)/5

Explanation:

First, define key terms:

• Term: A single number, variable, or product/quotient of numbers and variables, separated by +/-.
• Constant: A fixed number with no variable.
• Product: A multiplication of terms (e.g., $16abc$).
• Quotient: A division of terms (e.g., $\frac{3n}{4}$).
• Coefficient: A number multiplied by a variable.

Then categorize each expression:

1. $8b - 4$: 2 terms; has constant (-4); has coefficients (8, -4); no product/quotient.
2. $3x^2 + 15x + 1$: 3 terms; has constant (1); has coefficients (3, 15, 1); no product/quotient.
3. $3c - 2p + 6k - 12$: 4 terms; has constant (-12); has coefficients (3, -2, 6, -12); no product/quotient.
4. $\frac{3n}{4} + 7m$: 2 terms; has quotient ($\frac{3n}{4}$); has coefficients ($\frac{3}{4}$, 7); no product/constant.
5. $2 - (4w + 3y) = 2 -4w -3y$: 3 terms; has constant (2); has coefficients (-4, -3, 2); no product/quotient.
6. $16abc + 2d$: 2 terms; has product ($16abc$); has coefficients (16, 2); no constant/quotient.
7. $\frac{12b}{5}$: 1 term; has quotient ($\frac{12b}{5}$); has coefficient ($\frac{12}{5}$); no product/constant.

Answer:

Contains 2 or fewer terms:

$8b - 4$, $\frac{3n}{4} + 7m$, $16abc + 2d$, $\frac{12b}{5}$

Contains 3 or more terms:

$3x^2 + 15x + 1$, $3c - 2p + 6k - 12$, $2 - (4w + 3y)$

Contains a constant:

$8b - 4$, $3x^2 + 15x + 1$, $3c - 2p + 6k - 12$, $2 - (4w + 3y)$

Contains more than one product:

$16abc + 2d$

Contains at least one quotient:

$\frac{3n}{4} + 7m$, $\frac{12b}{5}$

Contains more than one coefficient:

$8b - 4$, $3x^2 + 15x + 1$, $3c - 2p + 6k - 12$, $\frac{3n}{4} + 7m$, $2 - (4w + 3y)$, $16abc + 2d$