The expression [tex]27x^{4} +15x^{3} +53x^{2}[/tex] is called as option d) Quartic Trinomial.
Step-by-step explanation:
The given expression is [tex]27x^{4} +15x^{3} +53x^{2}[/tex] .
To find the number of terms :
- one-term polynomial is called a monomial
- two-term polynomial is called a binomial and
- three-term polynomial is called a trinomial
"The number of terms in the expression is Three."
The three terms are as follows :
⇒ First term is [tex]27x^{4}[/tex]
⇒ Second term is 15x³
⇒ Third term is 53x²
Therefore, the given expression is called a "trinomial" with respect to the number of terms in it.
To find the degree :
The degree of a polynomial is the highest of the degrees of the individual terms in it with non-zero coefficients.
Here, in this expression [tex]27x^{4} +15x^{3} +53x^{2}[/tex] the highest degree is 4.
Fourth degree is known as "Quartic".
Now, combining the number of terms and degree in the given expression, it is known as "Quartic Trinomial" which is option D).
