Question

Which of the algebraic expressions are not linear expressions? Select all that apply. a. 3x - 2 b. -9y c. -7x^2^ + 4x d. -1/2x^2^ e. 8xy (The ^2^ means squared!)

Answer 1

c, d and e

Explanation:

A linear expression is an expression in which sum of exponents of variables is at most 1 in each of its terms.

Option a:
`3x - 2`

Here, the exponent of the variable is 1.

So, it is a linear expression.

Option b:
`-9y`

Here, the exponent of the variable is 1.

So, it is a linear expression.

Option c:
`-7x^2 + 4x`

Here, the highest exponent of the variable is 2.

So, it is NOT a linear expression.

Option d:
`-(1)/(2) x^2`

Here, the exponent of the variable is 2.

So, it is NOT a linear expression.

Option e:
`8xy`

Here, sum of exponents of variables is 2.

So, it is NOT a linear expression.

Hence, c, d and e are NOT algebraic expressions.