Question

select all the correct answers.
which polynomial expressions are in standard form?
□ $x^2 - x - 72$
□ $(x + 3)(x - 7)$
□ $-8x + 56$
□ $5$
□ $5x(2x)$

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written with terms in descending order of degree (exponent of the variable), and it is simplified (no factored form, no unmultiplied terms). Degree of a term is the exponent of the variable. For a constant (like 5), it can be considered as a polynomial of degree 0, which is in standard form.

Step2: Analyze each option

• \(x^{2}-x - 72\): The terms are in descending order of degree (degree 2, then degree 1, then degree 0 (constant -72)). It is simplified (not factored, no unmultiplied terms). So it is in standard form.
• \((x + 3)(x - 7)\): This is a factored form (product of two binomials), not in standard form (standard form is a sum of terms in descending degree). We would need to expand it to get it in standard form. So it is not in standard form.
• \(-8x+56\): The terms are in descending order of degree (degree 1, then degree 0 (constant 56)). It is simplified (not factored, no unmultiplied terms). So it is in standard form.
• \(5\): This is a constant polynomial (degree 0). A constant polynomial is in standard form (since there are no variables to order, and it is simplified). So it is in standard form.
• \(5x(2x)\): This has unmultiplied terms (the product of \(5x\) and \(2x\) is not yet simplified). Simplifying, we get \(10x^{2}\), but as given, it is not in standard form (it is a product, not a sum of terms in descending degree). So it is not in standard form.

Answer:

\(x^{2}-x - 72\), \(-8x + 56\), \(5\)