which polynomials are in standard form?\nchoose all answers that apply:\na 3z - 1\nb 2 + 4x - 5x²\nc -5p⁵ +…

Explanation:

Step1: Recall the definition of standard form of a polynomial

A polynomial is in standard form when its terms are written in descending order of degree.

Step2: Analyze option A

For the polynomial (3z - 1), the degree of the first term (3z) (where (z = z^{1})) is (1) and the degree of the second term (-1) (or (-1z^{0})) is (0). Since (1>0), the terms are in descending order of degree.

Step3: Analyze option B

For the polynomial (2 + 4x-5x^{2}), the degree of the first term (2) (or (2x^{0})) is (0), the degree of the second term (4x) (or (4x^{1})) is (1), and the degree of the third term (-5x^{2}) is (2). Since (0<1<2), the terms are not in descending order of degree.

Step4: Analyze option C

For the polynomial (-5p^{5}+2p^{2}-3p + 1), the degree of the first term (-5p^{5}) is (5), the degree of the second term (2p^{2}) is (2), the degree of the third term (-3p) (or (-3p^{1})) is (1), and the degree of the fourth term (1) (or (1p^{0})) is (0). Since (5 > 2>1>0), the terms are in descending order of degree.

Answer:

A. (3z - 1), C. (-5p^{5}+2p^{2}-3p + 1)