Question

question 21 of 25
which of the following are polynomials?
check all that apply.

a. \\(\frac{3}{5}x^4 - 18x^3 + x^2 - 10x + 3.5\\)

b. \\(3x^{-3} - 19\\)

c. \\(-x^3 + 5x^2 + 7x - 1\\)

d. \\(-x^3 + \sqrt{-x}\\)

e. \\(2x^2 + 5x - 3\\)

Explanation:

Step1: Recall polynomial definition

A polynomial is a sum of terms with non-negative integer exponents on variables, and coefficients can be real numbers.

Step2: Check Option A

$\frac{3}{5}x^4 -18x^3 +x^2 -10x +3.5$: All exponents are non-negative integers. Valid.

Step3: Check Option B

$3x^{-3} -19$: Has negative exponent $-3$. Invalid.

Step4: Check Option C

$-x^3 +5x^2 +7x -1$: All exponents are non-negative integers. Valid.

Step5: Check Option D

$-x^3 +\sqrt{-x}$: $\sqrt{-x}=(-x)^{1/2}$, exponent is not integer. Invalid.

Step6: Check Option E

$2x^2 +5x -3$: All exponents are non-negative integers. Valid.

Answer:

A. $\frac{3}{5}x^4 - 18x^3 + x^2 - 10x + 3.5$, C. $-x^3 + 5x^2 + 7x - 1$, E. $2x^2 + 5x - 3$