Question

which polynomials are in standard form? choose all answers that apply: a $3z - 1$ b $2 + 4x - 5x^2$ c $-5p^5 + 2p^2 - 3p + 1$ d none of the above

Explanation:

Step1: Recall standard form rule

A polynomial is in standard form when its terms are ordered from the highest degree to the lowest degree.

Step2: Check Option A

$3z - 1$ has terms ordered by degree: degree 1 ($3z$) then degree 0 ($-1$). This follows the standard form rule.

Step3: Check Option B

$2 + 4x - 5x^2$ has terms ordered from degree 0 to degree 2, which is reverse of the required order. It is not in standard form.

Step4: Check Option C

$-5p^5 + 2p^2 - 3p + 1$ has terms ordered by degree: degree 5 ($-5p^5$), degree 2 ($2p^2$), degree 1 ($-3p$), degree 0 ($1$). This follows the standard form rule.

Answer:

A. $3z - 1$
C. $-5p^5 + 2p^2 - 3p + 1$