Question
Students were asked to write an expression which then written in standard form would have a leading coefficient of three in a consistent term of -4, which of the following responses not necessarily a standard form yet is correct
Answers
GPT-4o mini
In mathematics, a polynomial expression is often written in standard form, which usually consists of arranging the terms in descending order of their degree and writing the leading coefficient in front.
If students were asked to write an expression that, when in standard form, has a leading coefficient of 3 and a consistent term of -4, an example of such an expression could be:
\[
3x^2 - 4
\]
In this case, the leading coefficient (the coefficient of the highest degree term, which is \(3\) for \(x^2\)) is \(3\), and the constant term (consistent term) is \(-4\).
Responses that are not necessarily in standard form but correctly hold the property of having a leading coefficient of 3 and a consistent term of -4 could be presented in other arrangements or forms. For instance:
1. \( 2x^3 + 3x^2 - 4 - x^3 \) (still equates to \(x^3 + 3x^2 - 4\))
2. \( 1.5x^4 + 1.5x^2 + -4 + 1.5x^2 -1.5x^4 \) (results in \( 1.5x^4 + 1.5x^2 - 4\) if properly combined).
Ultimately, as long as the leading coefficient of the term with the highest degree is 3 and one of the terms is a constant of \(-4\), the expression is valid, even if it's not in standard form.
If you have specific options to choose from or want clarification on anything else, feel free to share!
If students were asked to write an expression that, when in standard form, has a leading coefficient of 3 and a consistent term of -4, an example of such an expression could be:
\[
3x^2 - 4
\]
In this case, the leading coefficient (the coefficient of the highest degree term, which is \(3\) for \(x^2\)) is \(3\), and the constant term (consistent term) is \(-4\).
Responses that are not necessarily in standard form but correctly hold the property of having a leading coefficient of 3 and a consistent term of -4 could be presented in other arrangements or forms. For instance:
1. \( 2x^3 + 3x^2 - 4 - x^3 \) (still equates to \(x^3 + 3x^2 - 4\))
2. \( 1.5x^4 + 1.5x^2 + -4 + 1.5x^2 -1.5x^4 \) (results in \( 1.5x^4 + 1.5x^2 - 4\) if properly combined).
Ultimately, as long as the leading coefficient of the term with the highest degree is 3 and one of the terms is a constant of \(-4\), the expression is valid, even if it's not in standard form.
If you have specific options to choose from or want clarification on anything else, feel free to share!
A)3-2x^3-4x
B)4-7x+3x^3
C)7x^3-3x^4-4
D)-4x^2+3x^4-4
B)4-7x+3x^3
C)7x^3-3x^4-4
D)-4x^2+3x^4-4
Which one of those answer choices are correct