Savion Cameron

2022-12-18

Which polynomial is a quintic binomial?
A. ${\mathrm{x}}^{4}-2{\mathrm{x}}^{3}-{\mathrm{x}}^{2}+7\mathrm{x}+11$
B. ${\mathrm{x}}^{2}+4\mathrm{x}$
C. $3{\mathrm{x}}^{5}+2$
D. $5{\mathrm{x}}^{2}-2\mathrm{x}+1$

Kali Bates

Expert

Solution
The correct option is C
$3{\mathrm{x}}^{5}+2$
Explanation of the correct option:
Option C:
A polynomial of fifth-degree is called a quintic binomial.
So based on the question only $3{\mathrm{x}}^{5}+2$, which is a polynomial of degree $5$
Thus the polynomial $3{\mathrm{x}}^{5}+2$ is a quintic binomial.
So, the correct option is option C.
Thus, option C is the correct answer.
Explanation of the incorrect options:
Option A:
The polynomial ${\mathrm{x}}^{4}-2{\mathrm{x}}^{3}-{\mathrm{x}}^{2}+7\mathrm{x}+11$ is a polynomial of degree $4.$ And a fourth-degree polynomial is called a bi-quadratic polynomial.
So, option A is the incorrect option.
Option B:
The polynomial ${\mathrm{x}}^{2}+4\mathrm{x}$ is a polynomial of degree $2.$A second-degree polynomial is called a quadratic polynomial.
So, option B is the incorrect option.
Option D:
The polynomial $5{\mathrm{x}}^{2}-2\mathrm{x}+1$ is a polynomial of degree $2.$The second-degree polynomial is called a quadratic polynomial.
So, option D is the incorrect option.
Hence from the obtained information, only option C is correct.
Thus, option C is the correct option.

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