Given the polynomials, let's simplify the polynomials and label them.
Polynomial 1:
[tex]\begin{gathered} (x-\frac{1}{2})(6x+2) \\ \text{Simplify:} \\ 6x(x)+2x+6x(-\frac{1}{2})+2(-\frac{1}{2}) \\ \\ =6x^2+2x-3x-1 \\ \\ =6x^2-x-1 \end{gathered}[/tex]After simplifying, we have the simplified form:
[tex]6x^2-x-1[/tex]Since the highest degree is 2, this is a quadratic polynomial.
It has 3 terms, therefore by number of terms it is a trinomial.
Polynomial 2:
[tex]\begin{gathered} (7x^2+3x)-\frac{1}{3}(21x^2-12) \\ \\ \text{Simplify:} \\ (7x^2+3x)-7x^2+4 \\ \\ =7x^2+3x-7x^2+4 \\ \\ \text{Combine like terms:} \\ 7x^2-7x^2+3x+4 \\ \\ 3x+4 \end{gathered}[/tex]Simplified form:
[tex]3x+4[/tex]The highest degree is 1, therefore it is linear
It has 2 terms, therefore by number of terms it is a binomial
Polynomial 3:
[tex]\begin{gathered} 4(5x^2-9x+7)+2(-10x^2+18x-13) \\ \\ \text{Simplify:} \\ 20x^2-36x+28-20x^2+36x-26 \\ \\ \text{Combine like terms:} \\ 20x^2-20x^2-36x+36x+28-26 \\ \\ =2 \end{gathered}[/tex]Simplified form:
[tex]2[/tex]The highest degree is 0 since it has no variable, therefore it is a constant.
It has 1 term, by number of terms it is a monomial.
ANSWER:
Polynomial Simplified form Name by degree Name by nos. of ter
1 6x²-x-1 quadratic Trinomial
2 3x + 4 Linear Binomial
3 2 Constant Monomial