Which polynomials are in standard form? Choose two correct answers.

1. Understand Standard Form: A polynomial is in standard form when its terms are arranged in descending order of their exponents. For example, $ax^2 + bx + c$ is in standard form, while $c + bx + ax^2$ is not.

1. Examine the first polynomial: The first polynomial is $15x + 4$. The term $15x$ has an exponent of 1 for $x$ (since $x = x^1$), and the term $4$ has an exponent of 0 for $x$ (since $4 = 4x^0$). The exponents are 1 and 0, which are in descending order. Therefore, $15x + 4$ is in standard form.

1. Examine the second polynomial: The second polynomial is $12x$. This is a monomial with the exponent of $x$ being 1. It can be considered in standard form as it has only one term.

1. Examine the third polynomial: The third polynomial is $10x + 3x^2 - 8$. The terms have exponents of 1, 2, and 0 for $x$. To be in standard form, these should be arranged in descending order of exponents: $3x^2 + 10x - 8$. Since the given polynomial is not arranged in this order, it is not in standard form.

1. Examine the fourth polynomial: The fourth polynomial is $2 - 7x$. The terms have exponents of 0 and 1 for $x$. To be in standard form, these should be arranged in descending order of exponents: $-7x + 2$. Since the given polynomial is not arranged in this order, it is not in standard form.

1. Re-evaluate based on standard form definition: Let's re-examine the options with the strict definition of standard form (descending order of exponents).

• $15x + 4$: Exponents are 1 and 0. This is in descending order. So, it is in standard form.
• $12x$: Exponent is 1. This is in standard form.
• $10x + 3x^2 - 8$: Exponents are 1, 2, 0. Not in descending order. The standard form would be $3x^2 + 10x - 8$.
• $2 - 7x$: Exponents are 0, 1. Not in descending order. The standard form would be $-7x + 2$.

1. Consider the question's intent: The question asks to choose two correct answers. Often, single-term polynomials (monomials) are considered to be in standard form by default. However, the provided options suggest that we should look for polynomials where terms are ordered by descending exponent. Let's re-examine the third option: $10x + 3x^2 - 8$. If we rearrange it, we get $3x^2 + 10x - 8$. This is the standard form. The question might be asking which of the given expressions are in standard form as written. In that case, $15x + 4$ and $12x$ are the only ones that fit the definition of standard form as written.

8. Final check: A polynomial in standard form has its terms ordered from the highest degree to the lowest degree.
- $15x + 4$: Degree of $15x$ is 1, degree of $4$ is 0. Order: 1, 0. This is standard form.
- $12x$: Degree is 1. This is standard form.
- $10x + 3x^2 - 8$: Degrees are 1, 2, 0. Not in descending order. Standard form: $3x^2 + 10x - 8$.
- $2 - 7x$: Degrees are 0, 1. Not in descending order. Standard form: $-7x + 2$.

It seems there might be a misunderstanding in the provided options or the intended interpretation. However, based on the strict definition of standard form (descending order of exponents), only $15x + 4$ and $12x$ are in standard form as written. If the question implies that we should identify polynomials that can be rearranged into standard form, then all of them could be. Given the instruction to choose two, and the common understanding of standard form, $15x + 4$ and $12x$ are the most appropriate answers.