Question
Which polynomial is a quintic binomial?
Responses
3x5+2
3 x to the power of 5 end power plus 2
5x2−2x+1
5 x squared minus 2 x plus 1
x4+2x3−x2+7x+11
x to the power of 4 end power plus 2 x cubed minus x squared plus 7 x plus 11
x2+4x
Responses
3x5+2
3 x to the power of 5 end power plus 2
5x2−2x+1
5 x squared minus 2 x plus 1
x4+2x3−x2+7x+11
x to the power of 4 end power plus 2 x cubed minus x squared plus 7 x plus 11
x2+4x
Answers
GPT-4o mini
A quintic binomial is a polynomial that has a degree of 5 (quintic) and is made up of two terms (binomial).
Among the options provided:
1. **3x^5 + 2** - This is a quintic binomial because it has a degree of 5 and consists of two terms.
2. **5x^2 - 2x + 1** - This is a quadratic trinomial (degree 2) because it has three terms.
3. **x^4 + 2x^3 - x^2 + 7x + 11** - This is a polynomial of degree 4 with five terms, therefore not a quintic nor a binomial.
4. **x^2 + 4x** - This is a quadratic binomial (degree 2) consisting of two terms.
Thus, the polynomial that is a quintic binomial is **3x^5 + 2**.
Among the options provided:
1. **3x^5 + 2** - This is a quintic binomial because it has a degree of 5 and consists of two terms.
2. **5x^2 - 2x + 1** - This is a quadratic trinomial (degree 2) because it has three terms.
3. **x^4 + 2x^3 - x^2 + 7x + 11** - This is a polynomial of degree 4 with five terms, therefore not a quintic nor a binomial.
4. **x^2 + 4x** - This is a quadratic binomial (degree 2) consisting of two terms.
Thus, the polynomial that is a quintic binomial is **3x^5 + 2**.